Question

Find the nature of the roots of the quadratic equations $2x^2-\sqrt{5}x+1=0$.

Answer 1

Given,

$2x^2-\sqrt{5}x+1=0$

Determinant$=b^2-4ac$

To find nature of roots we need to find the determinant

$b^2-4ac=(\sqrt{5}{)}^2-4(1\left)\right(2)$

$5-8=-3$

As determinant is $-$ve.

The roots are imaginary.

$\therefore$ Nature of roots of $2a^2-\sqrt{5}x+1=0$ are imaginary.