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If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2

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Bunuel
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If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   29 Jan 2021, 23:21
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If 2 is a root of the equation \(x^2 + kx + 12 = 0\) and the equation \(x^2 + kx + q = 0\) has equal roots, what is the value of q?

A. 64
B. 32
C. 16
D. 8
E. 4
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C
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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   29 Jan 2021, 23:33
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\(x^2+kx+12=0\)

The root of the above equation is 2

\(2^2+k(2)+12=0\)

\(4+2k+12=0\)

\(2k=−16\)

\(k=−8\)

\(x^2+kx+q=0\)

\(x^2−8x+q=0\)

condition for equal roots is \(b^2-4ac=0\)

\((−8)^2=4(1)(q)\)

\(64=4q\)

\(q=16\)

Ans C
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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   30 Jan 2021, 08:58
x^2+kx+12=0 ---> if one of the roots is 2, then the 2nd root x2 will be 6. k=-(x1+x2)=-(2+6)=-8
x^2-8x+q=0 if this equation has equal roots, the root of this equation will be 4. Then q will be equal to 16. C)
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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   30 Jan 2021, 09:20
Asked: If 2 is a root of the equation \(x^2 + kx + 12 = 0\) and the equation \(x^2 + kx + q = 0\) has equal roots, what is the value of q?

4 + 2k + 12 = 0
k = -8

x^2 -8x + q = 0 has equal roots
q = 16


IMO C

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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   30 Jan 2021, 23:39
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'2' being the root of the equation hence substitute x = 2 in the equation \(x^2 + kx + 12 = 0\)

=> \(2^2 + 2k + 12 = 0\)

=> 4 + 2K + 12 = 0

=> 2k = -16

=> k = -8

Since, \(x^2 + kx + q = 0\) or \(x^2 - 8x + q\) has equal roots. Therefore, D(b^2 - 4ac) = 0

=> a = 1 ; b = -8 ; c = q

=> \((-8)^2 - 4(1)(q) = 0\)

=> 64 = 4q

=> q = 16

Answer C
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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   03 Feb 2021, 00:08
Hi can anyone explain how the answer is D?

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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink] New post   03 Feb 2021, 00:25
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Gargi1234 wrote:
Hi can anyone explain how the answer is D?

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The OA is C. Edited. Thank you.
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Re: If 2 is a root of the equation x^2 + kx + 12 = 0 and the equation x^2 [#permalink]
03 Feb 2021, 00:25
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