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If 2 is a Root of the Equation X2 + Ax + 12 = 0 and the Quadratic Equation X2 + Ax + Q = 0 Has Equal Roots, Then Q = - CBSE Class 10 - Mathematics

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Question

If 2 is a root of the equation x2 + ax + 12 = 0 and the quadratic equation x2 + ax + q = 0 has equal roots, then q =

  • 12

  • 8

  • 20

  • 16

Solution

x = 2is the common roots given quadric equation are `x^2 + ax + 12 = 0`, and  `x^2 + ax + q = 0`

Then find the value of q.

Here, `x^2 + ax + 12 = 0` ….. (1)

 `x^2 + ax + q = 0` ….. (2)

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

`2^2 + a xx 2 + 12 = 0`

          4 + 2a + 12 =0

                         2a =-16

                           a = -8

Now, putting the value of  a = - 8 in equation (2) we get

 `x^2 - 8x + q = 0`

Then,

`a_2 = 1,b_2 = -8 and , c_2 = q`

As we know that `D_1 = b^2 - 4ac`

Putting the value of  `a_2 = 1, b_2 = -8 and  c_2 = q`

`= (-8)^2 - 4 xx 1 xx q`

` = 64 - 4q`

The given equation will have equal roots, if D = 0

`64 - 4q = 0`

          `4q = 64`

            `q = 64/4`

            q = 16

  Is there an error in this question or solution?

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Solution If 2 is a Root of the Equation X2 + Ax + 12 = 0 and the Quadratic Equation X2 + Ax + Q = 0 Has Equal Roots, Then Q = Concept: Solutions of Quadratic Equations by Factorization.
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