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If 2 is a root of the equation $x 2$ + bx + 12 = 0 and the equation $x 2 + b x + q = 0$ has equal roots, then q =

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-8

-16

answer is A.

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Detailed Solution

Given:
2 is a root of the equation

x 2 + b x + 12 = 0

Substitute

x = 2

in the equation

x 2 + b x + 12 = 0

⇒ 4 + 2 b + 12 = 0 ⇒ 2 b + 16 = 0 ⇒ 2 b = − 16 ⇒ b = − 16 2 ⇒ b = − 8..... (1)

⇒

x 2 + b x + q = 0

becomes

x^{2} - 8 x + q = 0

Comparing

x 2 + b x + q = 0

with ax2+bx+c=0, we get
The value of a=1, b=-8, c=q
The roots of equation

x 2 + b x + q = 0

are equal.

⇒ D = 0 ⇒ b 2 − 4 a c = 0 ⇒ b 2 − 4 × 1 × q = 0

⇒ (− 8) 2 − 4 q = 0 (

since

b = − 8)

⇒ 64 = 4 q ⇒ q = 644 ⇒ q = 16

Hence, the correct option is 3.

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