# What is the discriminant of 3x^2-10x+4=0?

Sep 11, 2014

The discriminant is the expression ${b}^{2} - 4 a c$ where, $a , b \mathmr{and} c$ are found from the standard form of a quadratic equation, $a {x}^{2} + b x + c = 0$.

In this example $a = 3 , b = - 10 , \mathmr{and} c = 4$

${b}^{2} - 4 a c = {\left(- 10\right)}^{2} - 4 \left(3\right) \left(4\right) = 100 - 48 = 52$

Also note that the discriminant describes the number and type root(s).

${b}^{2} - 4 a c$ > 0, indicates 2 real roots

${b}^{2} - 4 a c$ = 0, indicates 1 real root

${b}^{2} - 4 a c$ < 0, indicates 2 imaginary roots