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If X = 1 is a Common Roots of the Equations Ax2 + Ax + 3 = 0 and X2 + X + B = 0, Then Ab = - CBSE Class 10 - Mathematics

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Question

If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + 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?

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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.
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