# What is the discriminant of -8x^2+4x−1 and what does that mean?

Apr 12, 2018

discriminant =$- 16$
It means that the polynomial has no real solutions

#### Explanation:

the discriminant is a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial
consider a function $a {x}^{2} + b x + c = 0$

in order to find the values of $x$ that satisfies the equation We use the following formula

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

where ${b}^{2} - 4 a c$ is the discriminant
if
${b}^{2} - 4 a c > 0$ then the equation has two real solutions
${b}^{2} - 4 a c = 0$ then the equation has one real solution
${b}^{2} - 4 a c < 0$ then the equation has no real solution

so in the equation $- 8 {x}^{2} + 4 x - 1 = 0$
by substituting in the discriminant formula with
$a = - 8 , b = 4 , c = - 1$

${b}^{2} - 4 a c = 16 - 4 \left(- 8 \times - 1\right) = - 16$$< 0$
so the functions will have no real solutions
(but it will have imaginary solutions)