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If X = 1 is a Common Root of Ax2 + Ax + 2 = 0 and X2 + X + B = 0, Then, Ab = - CBSE Class 10 - Mathematics

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Question

If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =

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Solution

x = 1 is the common roots given quadric equation are , ax2 + ax + 2 = 0 and x2 + x + b = 0

Then find the value of ab.

Here, ax2 + ax + 2 = 0 ….. (1)

 x2 + 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?

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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.
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