Equation Formula
The quadratic equation is one of the fundamental concepts in Algebra. This quadratic form can be solved and verified using formulas. These formulas must be retained by students if they are striving to excel in the subject of Mathematics. The Extramarks learning portal offers students comprehensive reference materials to facilitate learning the Equation Formula for them. Students can also attend interactive video lectures conducted by the mentors of Extramarks for an engaging and versatile learning experience.
Equation Problems
Students can examine quadratic Equation Formula solutions on the Extramarks educational website.
Solved Examples
2×2 – 5x + 2 = 0
Solution :
Comparing 2×2 – 5x + 2 = 0 and ax2 + bx + c = 0, one gets
a = 2, b = -5 and c = 2
Then,
x = [-b ± √b2 – 4ac] / 2a
x = [-(-5) ± √(-5)2 – 4(2)(2)] / 2(2)
x = [5 ± √(25 – 16)] / 4
x = [5 ± √9] / 4
x = [5 ± 3] / 4
x = (5 + 3) /4 and x = (5 – 3)/4
x = 8/4 and x = 2/4
x = 2 and x = 1/2
Therefore, the solution is {1/2, 2}.
√2f2 – 6f + 3√2 = 0
Solution:
Comparing √2f2 – 6f + 3√2 = 0 and ax2 + bx + c = 0, one gets
a = √2, b = -6 and c = 3√2
Then,
x = [-b ± √b2 – 4ac] / 2a
x = [-(-6) ± √(-6)2 – 4(√2)(3√2)] / 2(√2)
x = [6 ± √(36 – 24)] / 2√2
x = [6 ± √12] / 2√2
x = [6 ± 2√3] / 2√2
x = [6 + 2√3] / 2√2
x = 2(3 + √3) / 2√2
x = (3 + √3) / √2 |
x = [6 – 2√3] / 2√2
x = 2(3 – √3) / 2√2
x = (3 – √3) / √2 |
Therefore, the solution is {(3 + √3)/√2, (3 – √3)/√2}.
3y2 – 20y – 23 = 0
Solution:
Comparing 3y2 – 20y – 23 = 0 and ax2 + bx + c = 0, one gets
Then,
x = [-b ± √b2 – 4ac] / 2a
x = [-(-20) ± √(-20)2 – 4(3)(-23)] / 2(3)
x = [20 ± √(400 + 276)] / 6
x = [20 ± √676] / 6
x = [20 ± 26] / 6
x = [20 + 26] / 6
x = 46 / 6
x = 23 / 3 |
x = [20 – 26] / 6
x = -6 / 6
x = -1 |
Therefore, the solution is {-1, 23/3}.
36y2 – 12ay + (a2 – b2) = 0
Solution:
Comparing 36y2 – 12ay + (a2 – b2) = 0 and ax2 + bx + c = 0, one gets
a = 36, b = -12a and c = (a2 – b2)
Then,
x = [-b ± √b2 – 4ac] / 2a
x = [-(-12a) ± √(-12a)2 – 4(36)(a2 −b2)] / 2(36)
x = [12a ± √(144a2 – 144a2 + 144b2)] / 72
x = [12a ± √144b2] / 72
x = [12a ± 12b] / 72
x = 12(a ± b) / 72
x = (a ± b) / 6