Question

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

Answer 1

Based on quadratic equations of the form
`y = ax^2+bx+c`
the discriminant is
`Delta = b^2-4ac`
-this is taken from the component of the square root in the solution formula
`x= (-b+-sqrt(b^2-4ac))/(2a)`

For `y=x^2-8x+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
`(-b+-sqrt(b^2-4ac))/(2a)`
the roots are Integers.