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Question

The values of k for which the quadratic equation 16x2+4kx+9=0 has real and equal roots are

(a) 6, -16
(b) 36, −36
(c) 6, −6
(d) 34, -34


Solution

The given quadratic equation  16x2+4kx+9=0, has equal roots.

Here, a=16, b=4k and c=9.

As we know that D=b2-4ac

Putting the values of a=16, b=4k and c=9.

D=4k2-4169   =16k2-576

The given equation will have real and equal roots, if D = 0

Thus, 16k2-576=0
k2-36=0(k+6)(k-6)=0k+6=0 or k-6=0k=-6 or k=6

Therefore, the value of k is 6, −6.

Hence, the correct option is (c).


Mathematics
RD Sharma (2016)
Standard X

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