Question

Using quadratic formula solve the following equations.

(i) p² x² + (p² – q²)x – q² = 0

(ii) 9x² – 9 (a + b)x + (2a² + 5ab + 2b²) = 0

Answer 1

(i) p² x² + (p² – q²)x – q² = 0 

Comparing this with ax² + bx + c = 0, we have

a = p²

b = p² – q²

c = -q²

Δ = b² – 4ac

= (p² – q²)-4 x p² x -q²

= (p² – q²)² + 4p² q²

= (p² + q²)² > 0

So, the given equation has real roots given by

= 1

(ii) 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0

Comparing this with ax² + bx + c = 0.

a = 9

b = -9 (a + b)

c = (2a² + 5 ab + 2b²)

Δ = B² – 4AC

⇒ 81 (a + b)² – 36(2a² + 5ab + 2b²)

⇒ 9a² + 9b² – 18ab

⇒ 9(a – b)² > 0

∴ the roots are real and given by