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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

1 Answer

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Best answer

(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

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