Class 10 Maths- Solution of quadratic by factorization

Solution of quadratic by factorization

Let the quadratic equation be ax² + bx + c = 0, a ≠ 0.

Let the quadratic polynomial ax² + bx + c be expressible as the product of two linear factors, say (px + q) and (rx + s), where p, q, r, s are real numbers such that p ≠ 0 and r ≠ 0. Then,

ax² + bx + c = 0

Þ (px + q) (rx + s) = 0

Þpx + q = 0 or rx + s = 0

Solving these linear equations, we get the possible roots of the given quadratic equation as

Example: Solve the quadratic equation by factorization:

8x² – 22x – 21 = 0

Solution: we have,

8x² – 22x – 21 = 0

Þ 8x² – 28x + 6x – 21 = 0

Þ 4x (2x – 7) + 3 (2x – 7) = 0

Þ (2x – 7) (4x + 3) = 0

Þ 2x – 7 = 0 or, 4x + 3 = 0 Þ x 

Thus, x are two roots of the equation 8x² – 22x – 21 = 0