Question

Find the value(s) of k so that the quadratic equation $3x^2-2kx+12=0$ has equal roots.

Answer 1

The given quadratic equation is $3x^2-2kx+12=0$
On comparing it with the general quadratic equation $a{x}^2+bx+c=0$, we obtain
a = 3, b = -2k and c = 12
discriminant, 'D' of the given quadratic equation is given by
$D=b^2-4ac$
$=(-2k{)}^2$
$=4k^{2}144$
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
$4k^2-144=0$
$4(k^2-36)=0$
$k^2=36$
$k=\pm 6$
Thus, the values of k for which the quadratic equation $3x^2-2kx+12=0$ will have equal roots are 6 and .