Question

Determine the value of $k$ for which the quadratic equation $4x^2-3kx+1=0$ has equal roots.

• A. $\pm \frac{2}{3}$
• B. $\pm \frac{4}{3}$
• C. $\pm 4$
• D. $\pm 6$

Answer 1

Answer: (B)

$\pm \frac{4}{3}$

Nature of the roots for a quadratic equation $a{x}^2+bx+c=0$ , can be determined by its discriminant

$D=b^2-4ac$
Here, given quadratic equation is $4x^2-3kx+1=0$
Putting the value of $a,b,c$, we get
$D=(-3k{)}^2-4\times 4\times 1$
$\Rightarrow 9k^2-16=0$
$\Rightarrow 9k^2=16$
$\Rightarrow k^2=\frac{16}{9}$
$\Rightarrow k=\pm \frac{4}{3}$