Question

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

Answer 1

The given quadratic equation is 3x² − 2kx + 12 = 0

On comparing it with the general quadratic equation ax² + b x + c = 0, we obtain

a = 3, b = −2k and c = 12

Discriminant, ‘D’ of the given quadratic equation is given by

D = b² − 4ac

= (− 2k)² − 4 × 3 × 12

= 4k² − 144

For equal roots of the given quadratic equations, Discriminant will be equal to 0.

i.e., D = 0

`rArr 4k^2-144=0`

`rArr4(k^2-36)=0`

`rArrk^2=36`

`rArrk=+-6`

Thus, the values of k for which the quadratic equation 3x² − 2kx + 12 = 0 will have equal roots are 6 and −6.