#### Question

If x = 1 is a common roots of the equations ax^{2} + ax + 3 = 0 and x^{2} + x + b = 0, then ab =

3

3.5

6

-3

#### Solution

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`

Is there an error in this question or solution?

#### APPEARS IN

Solution If X = 1 is a Common Roots of the Equations Ax2 + Ax + 3 = 0 and X2 + X + B = 0, Then Ab = Concept: Solutions of Quadratic Equations by Factorization.