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.
$\therefore\left(b^{2}-4 a c\right)=0$
$\Rightarrow(3 k)^{2}-4 \times 4 \times 1=0$
$\Rightarrow 9 k^{2}=16$
$\Rightarrow k^{2}=\frac{16}{9}$
$\Rightarrow k=\pm \frac{4}{3}$
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