Without solving, determine the nature of the roots of:

$x^2-5x+6=0$;
$4x^2+4x+1=0$;
$2x^2+x+3=0$.

Show the discriminant in each case.

Question

Without solving, determine the nature of the roots of: $x^2-5x+6=0$; $4x^2+4x+1=0$; $2x^2+x+3=0$. Show the discriminant in each case.

Accepted Answer

(a) $\Delta=1$: Distinct real; (b) $\Delta=0$: Equal real; (c) $\Delta=-23$: No real roots.

Quadratic Functions, Equations and Inequalities