Question

the roots of 3y ^2 + ky + 12 = 0 real and unequal then find k

Answer 1

it is given that roots are real and distinct then discriminant of the equation should be greater than 0

b^2-4ac >0

k^2-4.3.12>0

k^2>4.3.12

k^2>12.12

-12<k<12

the requires values of k are (-12,12)

Answer 2

$3y {}^{2} + ky + 12 = 0$
$for \: real \: and \: unequal \: roots$
$d > 0$
$d = b {}^{2} - 4ac$
$k {}^{2} - 4(3)(12) > 0$
$k {}^{2} - 144 > 0$
$k {}^{2} > 144$
$k > 12$
$so \: k = 12$

$thanks$