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

1 Answer
Alan P.
Apr 29, 2015

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.

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