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

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-16

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Solution

The correct option is C 16
Given equation $x^{2} + b x + 12 = 0$
one root is 2
So,put x=2
4+2b+12=0
2b=-16
b=-8
Now roots of equation $x^{2} + b x + q = 0$ are equal
So, D=0
$b^{2} - 4 q = 0$
${(- 8)}^{2} - 4 q = 0$
$4 q = 64 \Rightarrow q = 16$

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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=

The correct option is C 16Given equation x2+bx+12=0one root is 2So,put x=24+2b+12=02b=-16b=-8Now roots of equation x2+bx+q=0 are equal So, D=0b2−4q=0(−8)2−4q=04q=64⇒q=16

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

The correct option is C 16
Given equation $x^{2} + b x + 12 = 0$
one root is 2
So,put x=2
4+2b+12=0
2b=-16
b=-8
Now roots of equation $x^{2} + b x + q = 0$ are equal
So, D=0
$b^{2} - 4 q = 0$
${(- 8)}^{2} - 4 q = 0$
$4 q = 64 \Rightarrow q = 16$