Question

If x = 1 is a common roots of the equations ax² + ax + 3 = 0 and x² + x + b = 0,  then ab =

Options

• 3

• 3.5

• 6

• -3

Answer 1

 x = 1is the common roots given quadric equation are `ax^2 + ax + 3 = 0`, and `x^2 + x + b= 0`

Then find the value of q.

Here, `ax^2 + ax + 3 = 0 `….. (1)

`x^2 + x + b = 0`….. (2)

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

`a xx 1^2 + a xx 1 +3 = 0`

                 `a+a + 3 = 0`

                               `2a = -3`

                                 `a = -3/2`

Now, putting the value of x = 1 in equation (2) we get

`1^2 + 1+b = 0`

         `2 +b = 0`

                 `b = -2`

Then,

`ab = (-3)/2 xx (-2)`

    `=3`