#### Question

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

12

8

20

16

#### Solution

x = 2is the common roots given quadric equation are `x^2 + ax + 12 = 0`, and `x^2 + ax + q = 0`

Then find the value of *q.*

Here, `x^2 + ax + 12 = 0` ….. (1)

`x^2 + ax + q = 0` ….. (2)

Putting the value of x = 2 in equation (1) we get

`2^2 + a xx 2 + 12 = 0`

4 + 2a + 12 =0

2a =-16

a = -8

Now, putting the value of a = - 8 in equation (2) we get

`x^2 - 8x + q = 0`

Then,

`a_2 = 1,b_2 = -8 and , c_2 = q`

As we know that `D_1 = b^2 - 4ac`

Putting the value of `a_2 = 1, b_2 = -8 and c_2 = q`

`= (-8)^2 - 4 xx 1 xx q`

` = 64 - 4q`

The given equation will have equal roots, if D = 0

`64 - 4q = 0`

`4q = 64`

`q = 64/4`

** q = 16**