Question

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

Options

• 8

• -8

• 16

• -16

Answer 1

2 is the common roots given quadric equation are  x² + bx + 12 = 0 and  x² + bx + q = 0 

Then find the value of q.

Here,  x² + bx + 12 = 0 ….. (1)

x² + bx + q = 0 ….. (2)

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

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

         `4 + 2b + 12 = 0`

                          `2b = - 16`

                            `b = -8`

Now, putting the value of b = -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`