# How do you find the discriminant and how many solutions does 5w^2-2w+4=0  have?

${b}^{2} - 4 a c = - 76$, two complex conjugate roots

#### Explanation:

$5 {w}^{2} - 2 w + 4 = 0$

Comparing the above equation with the standard quadratic equation: $a {x}^{2} + b x + c = 0$ we get

$a = 5 , b = - 2$ & $c = 4$

hence the discriminant ${b}^{2} - 4 a c$ of given quadratic equation is given as

${b}^{2} - 4 a c = {\left(- 2\right)}^{2} - 4 \left(5\right) \left(4\right)$

$= - 76 < 0$

$\because {b}^{2} - 4 a c < 0$ hence given quadratic equation has two conjugate complex roots.