# How do you find the discriminant and how many solutions does -5x^2+7x-2=0 have?

Apr 30, 2015

Discriminant $D = {d}^{2} = {b}^{2} - 4 a c = 49 - 40 = 9$ --> d = 3 and d = -3.
There are 2 solutions, called real roots of the quadratic equations.

$x 1 = - \frac{b}{2 a} + \frac{d}{2 a} = \frac{7}{10} - \frac{3}{10} = \frac{4}{10} = \frac{2}{5}$

$x 2 = - \frac{b}{2} a - \frac{d}{2} a = \frac{7}{10} + \frac{3}{10} = \frac{10}{10} = 1$

Note . We can use shortcut to quickly solve this equation.

Since a + b + c = 0, then one real root is 1 and the other is $\left(\frac{c}{a} = \frac{- 2}{-} 5 = \frac{2}{5}\right)$.
When a - b + c = 0, then one real root is (-1) and the other is $\left(- \frac{c}{a}\right)$.