Question

Determine the nature of roots of the following equations from the discriminant:

$2x^2+5\sqrt{3}x+16=0$

• A. real and equal
• B. real and unequal
• C. non real
• D. Cannot be determined

Answer 1

Answer: (C)

non real

Given equation is, $2x^2+5\sqrt{3}x+16=0$
We know, $D=b^2-4ac$
$a=1,b=5\sqrt{3},c=16$

$D=(5\sqrt{3}{)}^2-4\times 16\times 2$
$D=75-128$
$\therefore D=-53$
Since, $D<0$.

The roots arnon real.