Here you will learn how to find solution of quadratic equation of class 10 and different methods used to solve quadratic equation.
Let’s begin –
Solution of Quadratic Equation Class 10
(a) The general form of quadratic equation is ax2+bx+c = 0, a ≠ 0.
The roots or solution of quadratic equation can be found in following manner.
a(x2+bax+ca) = 0 ⟹ (x+b2a)2 + ca – b24a2 = 0
(x+b2a)2 = b24a2 – ca
⟹ x = −b±√b2–4ac2a
This −b±√b2–4ac2a expression can be directly used to find the two roots of a quadratic equation. This formula is known as sridharacharya formula.
(b) This expression b2–4a = D is called the discriminant of the quadratic equation.
Example : Find the roots of the quadratic equation x2+3x+2 = 0. Also find sum of roots and product of roots.
Solution : We have, x2+3x+2 = 0
By using the formula described above,
x = −3±√9–82 = −3±12
⟹ x = -1 and -2
Let α = -1 and β = -2
Sum of Roots = α+β = -3
Product of Roots = αβ = 2
Different Methods for Solving Quadratic Equation
Following three methods are used to solve quadratic equation. These methods are discussed in detail in next sections.
(1) By the method of factorisation.