Determine the Nature of the Roots Using the Discriminant -4x^2+7x-3=0

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant ${\displaystyle \left(\Delta \right)}$:

${\displaystyle \Delta >0}$ means there are ${\displaystyle 2}$ distinct real roots.

${\displaystyle \Delta =0}$ means there are ${\displaystyle 2}$ equal real roots, or ${\displaystyle 1}$ distinct real root.

${\displaystyle \Delta <0}$ means there are no real roots, but ${\displaystyle 2}$ complex roots.

Since the discriminant is greater than ${\displaystyle 0}$, there are two real roots.

Two Real Roots