
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Discriminant Formula
The Discriminant Formula is used to determine how many solutions a quadratic problem has. In Algebra, the Discriminant Formula is the term that occurs in the quadratic formula under the square root (radical) sign.
A polynomial’s Discriminant Formula is a function of its coefficients and is symbolised by the capital ‘D’ or Delta sign (Δ). Discriminant Formula demonstrates the nature of the roots of any quadratic equation with rational values a, b, and c. A quadratic equation may simply indicate the actual roots or the number of xintercepts. This formula is used to determine if the quadratic equation’s roots are real or imaginary.
The Discriminant Formula is a significant mathematical theme.
Formula for Discriminant
D = b2 – 4ac is the Discriminant Formula for a quadratic equation ax2 + bx + c = 0. Due to the fact that the degree of a quadratic equation is 2, students know that it can only have two roots. Students already know that the quadratic formula is used to solve the quadratic equation ax2 + bx + c = 0. The quadratic formula may be used to get the roots: x = [b ± √ (b2 – 4ac) ] / [2a]. The discriminant D is b2 – 4ac in this case, and it is contained within the square root. As a result, the quadratic formula is x = [b ± √D] / [2a]. In this case, D might be either > 0, = 0, or 0. In each of these circumstances, let students identify the nature of the roots.
 If Discriminant Formula > 0, the quadratic formula is x = [b ± √(positive number)] / [2a], then the quadratic equation has two unique real roots.
 If Discriminant Formula = 0, the quadratic formula becomes x = [b] / [2a], and the quadratic equation has just one real root in this instance.
 If Discriminant Formula is 0, the quadratic formula is x = [b ± √(negative number)] / [2a]. As a result, the quadratic equation has two unique complex roots in this situation (since the square root of a negative number yields an imaginary number). For instance, √(4) = 2i).
What Is Discriminant Formulas?
In Mathematics, a Discriminant Formula is a parameter of an object or system that is estimated to help in its categorization or solution. The discriminant for a quadratic equation ax2 + bx + c = 0 is b2 4ac; for a cubic equation x3 + ax2 + bx + c = 0, it is a2b2 + 18abc 4b3 4a3c 27c2. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct; if the Discriminant Formula is zero, the roots are real with at least two equals; and if the discriminant is negative, the roots contain a conjugate pair of complex roots. For the generic quadratic, or conic, equation ax2 + bxy + cy2 + dx + ey + f = 0, a Discriminant Formula may be determined; it determines whether the conic represented is an ellipse.
Why is Discriminant Formula Important?
Discriminant Formula for elliptic curves, finite field extensions, quadratic forms, and other mathematical entities are also specified. Differential equation discriminants are algebraic equations that disclose information about the families of solutions to the original equations.
Discriminant Formula of a Quadratic Equation
The most fundamental approach for obtaining the roots of a quadratic problem is the Quadratic Formula. Certain quadratic equations are difficult to factor, therefore students can utilise this quadratic formula to determine the roots as rapidly as possible. The quadratic equation’s roots may also be used to calculate the sum and product of the quadratic equation’s roots. The two roots of the quadratic formula are presented as a single statement. To derive the equation’s two separate roots, apply the positive and negative signs alternately.
The Quadratic Formula is the most fundamental approach for obtaining the roots of a quadratic problem. Certain quadratic equations are difficult to factor, therefore students can use this quadratic formula to rapidly discover the roots. The roots of a quadratic equation may also be utilised to compute the sum and product of the roots of a quadratic equation. The quadratic formula’s two roots are provided as a single equation. Use the positive and negative signs alternately to generate the equation’s two separate roots.
The sum and product of the quadratic equation’s roots may be calculated using the coefficient of x2, x term, and constant term of the quadratic equation ax2 + bx + c = 0. The sum and product of the roots of a quadratic equation may be determined simply from the equation without solving it. The sum of the roots of the quadratic equation is the inverse of the coefficient x divided by the coefficient x2. The product of the constant term and the coefficient of x2 equals the product of the equation’s root.
Discriminant Formula of a Cubic Equation
In Analytical Geometry, the graph of every quadratic function is a parabola in the xy plane. Assume a quadratic polynomial of the form The numbers h and k are the Cartesian coordinates of the vertex (or stationary point). In other words, k is the quadratic function’s minimum (or maximum, if a 0), and h is the xcoordinate of the axis of symmetry (i.e., the axis of symmetry has equation x = h).
Examples Using Discriminant Formulas
The Discriminant Formula may be used to identify the number of roots in a quadratic equation. A discriminant might be positive, negative, or nil. The nature of roots may be determined by knowing the value of a determinant as follows:
If the Discriminant Formula is positive, there are two different and actual solutions to the quadratic equation.
When the Discriminant Formula value is zero, the quadratic equation has either one or two real and equal solutions.
If the Discriminant Formula value is negative, there are no actual solutions to the quadratic equation.
The Discriminant formula is used to determine the discriminant of a polynomial equation. The discriminant of a quadratic equation, in particular, is used to identify the number and type of roots. The discriminant of a polynomial is a function composed of the polynomial’s coefficients. Let students go through the Discriminant Formula and some solved examples.
FAQs (Frequently Asked Questions)
1. Where can students learn more about Discriminant Formulas?
Students may learn everything they need to know about the Discriminant Formula by visiting the Extramarks website. Extramarks also has a mobile application via which students may access all of the information that is available on the website. All of the content on the platforms has been given by highly certified teachers who have years of relevant teaching experience. They have taught students about the Discriminant Formula, therefore they are quite aware of all of the challenges that students confront with regard to the process of learning.