Question

If 1 is a root of the quadratic equation 3x² + ax - 2 = 0 and the quadratic equation a(x² + 6x) - b = 0 has equal roots, find the value of b.

Answer 1

For a quadratic equation, ax² + bx + c = 0, 

D = b² – 4ac 

If D = 0, roots are equal 

Given, 

1 is a root of the quadratic equation 3x² + ax - 2 = 0

⇒ 3 + a – 2 = 0 

⇒ a = -1 

Now, 

the quadratic equation a(x² + 6x) - b = 0 has equal roots

⇒ x² + 6x + b = 0 has equal roots 

⇒ D = 36 – 4b = 0 

⇒ b = 9