#### Question

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

1

2

3

4

#### Solution

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

Then find the value of *ab.*

Here, ax^{2} + ax + 2 = 0 ….. (1)

x^{2} + x + b = 0….. (2)

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

`1^2 + 1+b = 0`

`2 + b = 0`

` b = -2`

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

`a + a + 2 = 0`

` 2a + 2 = 0`

`a = (-2)/2`

`=-1`

Then, `ab = (-1) xx (-2)`

= 2

Is there an error in this question or solution?

#### APPEARS IN

Solution If X = 1 is a Common Root of Ax2 + Ax + 2 = 0 and X2 + X + B = 0, Then, Ab = Concept: Solutions of Quadratic Equations by Factorization.