Question

Find the values of $k$ for which the equation $5x^2-kx+4=0$ has real roots.

• A. $k\le -4\sqrt{5}$
• B. $k\ge 4\sqrt{5}$
• C. $k=2$
• D. $k=-2$.

Answer 1

Answer: (A), (B)

The correct options are
A $k\le -4\sqrt{5}$
B $k\ge 4\sqrt{5}$

Given equation is
$5x^2-kx+4=0$

Now for real roots to exist :

$D\ge 0$

$\Rightarrow b^2-4ac\ge 0$

Hence,

$k^2-4\left(20\right)\ge 0$

$\Rightarrow k^2\ge 80$

$\Rightarrow k\ge 4\sqrt{5}$ or $k\le -4\sqrt{5}$

Hence, options A and B are correct.