Question

For what values of k the quadratic equation 12x^2+4kx+3=0 had equal zeroes?????????????????.

Answer 1

HERE IS THE SOLUTION;

◆ If this equation has equal roots, then the D=0.

So, here

a = 12, b=4k, c=3

$b {}^{2} - 4ac = 0 \\ \\ (4k) {}^{2} = 4(12)(3) \\ \\ = > 16k {}^{2} = 144 \\ \\ = > k {}^{2} = \frac{144}{16 } \\ \\ = > k {}^{2} = 9 \\ \\ = > k = 3$

◆ So the value of k is 3.

HOPE IT HELPS

Answer 2

HELLO FRIEND

FOR EQUAL ROOTS DISCRIMINANT MUST BE EQUALS TO ZERO

SO , THE VALUE OF D i.e
$\: d \: \: = \: b ^{2} \: - \: 4ac \: \:$
SO , PUT D = 0

THEN
$(4k)^{2} \: - \: 4 \times 12 \times 3 \: \: = \: \: 0$
$16 {k}^{2} \: \: - \: \: 144 \: \: = \: \: 0 \\ {k}^{2} \: \: = \: \: 144 \: \div 16\\ k ^{2} \: \: \ = \: \: 9\\ then \\ k \: = \: \: \sqrt{9} \\ k \: \: = \: \: 3$
$k \: \: = \: \: \sqrt{9} \: \\ k \: \: = \: \: 3$

I HOPE YOU MAY UNDERSTAND THE ANSWER.