# What is the discriminant of 7x^2+8x+1=0 and what does that mean?

Jul 25, 2015

Solve $y = 7 {x}^{2} + 8 x + 1 = 0$

Answer: -1 and $- \frac{1}{7}$

#### Explanation:

$D = {d}^{2} = {b}^{2} - 4 a c = 64 - 56 = 8 > 0$. This means there are 2 real roots (2 x-intercepts).
In this case (a - b + c = 0) we'd better use the shortcut --> two real roots: -1 and $\left(- \frac{c}{a} = - \frac{1}{7}\right)$
REMINDER OF SHORTCUT
When a + b + c = 0 -> 2 real roots: 1 and c/a
When a - b + c = 0 -> 2 real roots: -1 and -c/a