Question

Find the discriminant of the following quadratic equations and hence determine the nature of the roots of the equation :
$x^2+x+\frac{1}{4}=0$

Answer 1

Given equation: $x^2+x+\frac{1}{4}=0$

$\Rightarrow 4x^2+4x+1=0$

$a=4,b=4,c=1$

$D=b^2-4ac$

$⟹D=(4{)}^2-4(4\left)\right(1)$

$⟹D=16-16$

$⟹D=0$

Thus $D=0$

$\therefore$ Only one real zero.