Question

If 2 is a root of the equation x² + ax + 12 = 0 and the quadratic equation x² + ax + q = 0 has equal roots, then q

A. 12

B. 8

C. 20

D. 16

Answer 1

The given equation x² + ax + 12 = 0 has a root = 2 

So it will satisfy the equation 

4 + 2a + 12 = 0 

2a + 16 = 0 

a = – 8 

Putting value of a in second equation, it becomes 

x² + ax + q = 0 

x² – 8x + q = 0 

Roots are equal so d = 0 

⇒ b² – 4ac = 0 

⇒ 64 – 4q = 0 

⇒ q = 64/4 

⇒ q = 16