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29 Jan 2021, 23:21
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C
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Difficulty:
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73% (01:50) correct
27%
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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
A. 64
B. 32
C. 16
D. 8
E. 4
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
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
30 Jan 2021, 08:58
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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)
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)
