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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

ConceptSolutions of Quadratic Equations by Factorization

#### 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?

#### APPEARS IN

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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