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# If 2 is a Root of the Equation X2 + Bx + 12 = 0 and the Equation X2 + Bx + 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 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =

• 8

• -8

• 16

• -16

#### Solution

2 is the common roots given quadric equation are  x2 + bx + 12 = 0 and  x2 + bx + q = 0

Then find the value of q.

Here,  x2 + bx + 12 = 0 ….. (1)

x2 + bx + q = 0 ….. (2)

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

2^2 + b xx 2 + 12 = 0

4 + 2b + 12 = 0

2b = - 16

b = -8

Now, putting the value of b = -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 + Bx + 12 = 0 and the Equation X2 + Bx + Q = 0 Has Equal Roots, Then Q = Concept: Solutions of Quadratic Equations by Factorization.
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