Cubic Equation Formula
Cubic Equation Formula
The cubic equation is represented by the Cubic Equation Formula. A cubic polynomial, often known as a cubic equation, is a three-degree polynomial. Cubic equations can have up to three real roots and must have at least one real root. A Cubic Equation Formula root can also be imaginary, but at least one of them must be real. Below is an explanation of the Cubic Equation Formula and a few instances with solutions. Learners can explore them.
A mathematical statement including a “equal to” sign between two algebraic expressions with equal values is called an equation. Based on the degree of the equation, there are three types of equations in algebra: linear, quadratic, and cubic. All of these formulae and equations, along with the cubic equation formula, will be covered in detail here.
A quadratic equation is one in which the degree of the equation is two, whereas a linear equation is one in which the highest power of the variable or the equation degree is one. A cubic equation has a variable or equation degree with a maximum power of three.
What is Cubic Equation Formula?
The cubic equation curve can also be derived using the Cubic Equation Formula. Finding the roots of a Cubic Equation Formula is made much easier by adopting a cubic equation representation. An n-degree polynomial will have n zeros or roots. The cubic equation is expressed as ax3+bx2+cx+d=0.
In mathematics, the cubic equation is expressed by the Cubic Equation Formula. A Cubic Equation Formula is one that has degree three. All cubic equations have roots that are either one real root and two imaginary roots, or three real roots in nature. Three-degree polynomials are referred to as cubic polynomials.
Traditionally, a cubic problem is resolved by first converting it into a quadratic equation, which is then factored or solved using the quadratic formula.
Similar to how a quadratic equation has two real roots, a cubic equation may have three. A cubic equation, on the other hand, has at least one real root, as opposed to a quadratic equation, which occasionally may not have a genuine solution. The other two roots could be made up or real.
Any equation, whether it be a cubic equation, must first be put into a standard form. Understanding this formula is crucial for students, and learning from the Extramarks platform can be a helpful option for them.
Depressing the Cubic Equation
Students need the Cubic Equation Formula in order to plot the curve of a cubic equation. This Cubic Equation Formula aids in locating a cubic equation’s roots. There will be n number of roots if the polynomial has degree n. The zeros are another name for the cubic equation’s roots.
Students will have read about cubic equations in the article on the Extramarks website and mobile application. An algebraic equation with the degree of equation 3 is called a cubic equation.
The solution to a cubic equation will then be covered. Experts have also discussed using a graphical approach to solve an issue involving a cubic equation. Finally, they discovered the connection between a cubic equation’s coefficients and roots, as well as its proof. Students can better understand the cubic equation formula by using examples with solutions.
The many kinds of equations are as follows:
There are three main types of equations in Mathematics.
- 1. Linear equation
- 2. Quadratic equation
- 3. Cubic Equation
A Cubic Equation Formula is one in which the variable can vary by three steps. To put it another way, a Cubic Equation Formula is one in which the variable has the maximum degree of three.
The Cubic Equation’s General Form
A Cubic Equation Formula has the generic form an x3 + b x2 + cx + d = 0. Here, a, b, c, and d are constants with a 0, and x is a variable. There will be three solutions that fulfil a Cubic Equation Formula. They could be equal or not.
Examples Using Cubic Equation Formula
- Find the following cubic equation’s roots. 2×3 + 3×2 – 11x – 6 = 0
Solution: To find: The given equation’s roots.
We will utilize the trial-and-error method to identify one root because the factorization method cannot be used to solve this equation.
Usually, we start with the number “1.”
f (1) = 2 + 3 – 11 – 6 ≠ 0\sf (–1) = –2 + 3 + 11 – 6 ≠ 0\sf (2) = 16 + 12 – 22 – 6 = 0
Value “2” makes the L.H.S equal to “0”. Hence two is one of the three roots.
Now we will use Synthetic Division Method to find the other two roots.
We divide our equation by (x-2) and the quotient will give us the other two roots. We divide our equation by (x-2) and the quotient will give us the other two roots.
Quotient : (2×2 + 7x + 3)
Factorising this quotient,
(2x+1) (x+3)
From here we get the values of x as,
x = -1/2 and x = -3
- Pick one of the following cubic polynomials:
Answer:
- p(x) = 5×2 + 6x + 1; q(z) = z2 1; r(z) = z2 + (2); p(x) = 2x + 3;
- 6 q(y): 81y3 1 r(z): z + 3 s(x): 10x p(y): y3 6y2 + 11y
- What is a Cubic Equation Formula?
Answer: An Cubic Equation Formula of degree three is called a cubic equation. A cubic equation has the conventional form ax3+bx2+cx+d=0.
- How can students determine the cubic equation’s roots?
The methods for locating the roots of the cubic equation are as follows:
- Utilizing Factor Lists to Find Integer Solutions
- Graphical Methodology
- How many roots may a cubic equation have?
Answer: A cubic equation has three roots. The roots of a cubic equation could be in any of the following situations:
- All three roots could be unique and real.
- Two of the three roots might be equal and all three could be true.
- All three roots may exist and be equivalent.
- The other two roots may not be real, but one of them may be (complex).
- How can students tell if a mathematical equation is cubic?
Answer: If the equation has a maximum degree of three, it is a cubic equation.
