Question

If 3 and –3 are the solutions of equation ax² + bx – 9 = 0. Find the values of a and b.

Answer 1

For x = 3 and x = –3 to be solutions of the given quadratic equation, it should satisfy the equation

So, substituting x = 3 and x = –3 in the given equation, we get

a(3)² + b(3) – 9 = 0

`\implies` a(9) + b(3) – 9 = 0

`\implies` 9a + 3b – 9 = 0  ...(1)

a(–3)² + b(–3) – 9 = 0

`\implies` a(9) + b(3) – 9 = 0 

`\implies` 9a – 3b – 9 = 0  ...(2)

Solving equations (1) and (2) simultaneously,

9a + 3b – 9 = 0  ...(1)

9a – 3b – 9 = 0  ...(2)

(1) + (2)

`\implies` 18a – 18 = 0

`\implies` a = 1

Substitute in (2)

`\implies` b = 0