# How do you find the discriminant and how many and what type of solutions does y=x^2-8x+7 have?

Apr 29, 2015

Based on quadratic equations of the form
$y = a {x}^{2} + b x + c$
the discriminant is
$\Delta = {b}^{2} - 4 a c$
-this is taken from the component of the square root in the solution formula
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

For $y = {x}^{2} - 8 x + 7$
$\Delta = 64 - 28 = 36$

Since $\Delta > 0$
there are two roots
and since $\Delta = {6}^{2}$
the roots are Rational.

In fact based on the full form of
$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
the roots are Integers.