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Question

Find the value(s) of k so that the quadratic equation 3x22kx+12=0 has equal roots.

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Solution

The given quadratic equation is 3x22kx+12=0
On comparing it with the general quadratic equation ax2+bx+c=0, we obtain
a = 3, b = -2k and c = 12
discriminant, 'D' of the given quadratic equation is given by
D=b24ac
=(2k)2
=4k2144
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
4k2144=0
4(k236)=0
k2=36
k=±6
Thus, the values of k for which the quadratic equation 3x22kx+12=0 will have equal roots are 6 and .


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