If the equation
Question:

If the equation $4 x^{2}-3 k x+1=0$ has equal roots, then $k=$ ?

(a) $\pm \frac{2}{3}$

(b) $\pm \frac{1}{3}$

(c) $\pm \frac{3}{4}$

(d) $\pm \frac{4}{3}$

Solution:

(d) $\pm \frac{4}{3}$

It is given that the roots of the equation $\left(4 x^{2}-3 k x+1=0\right)$ are equal.

$\therefore\left(b^{2}-4 a c\right)=0$

$\Rightarrow(3 k)^{2}-4 \times 4 \times 1=0$

$\Rightarrow 9 k^{2}=16$

$\Rightarrow k^{2}=\frac{16}{9}$

$\Rightarrow k=\pm \frac{4}{3}$