Find the values of $k$ for which the given equation has real and equal roots
$12 x^{2} + 4 k x + 3 = 0$

Open in App

Solution

The given equation is $12 x^{2} + 4 k x + 3 = 0$

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

$∴ D = b^{2} - 4 a c = {(4 k)}^{2} - 4 \times 12 \times 3 = 16 k^{2} - 144$

The given equation will have real and equal roots, if

$D = 0 \Rightarrow 16 k^{2} - 144 = 0 \Rightarrow k^{2} = 9 \Rightarrow k = \pm 3$

Suggest Corrections

Similar questions

k

(k - 12) x^{2} + 2 (k - 12) x + 2 = 0

k

x^{2} - 4 k x + k = 0

16 x^{2} + 4 k x + 9 = 0

6, - \frac{1}{6}

\frac{3}{4}, - \frac{3}{4}

Join BYJU'S Learning Program