How to use the discriminant to find out what type of solutions the equation has for x^2 - 8x + 3 = 0?

1 Answer
Alan P.
May 23, 2015

For a quadratic of the form
ax^2 +bx+c=0
the discriminant is
Delta = b^2-4ac
where
Delta { (<0 rarr "no Real solutions"),(=0 rarr "1 Real solution"),(>0 rarr "2 Real solutions"):}

Given
x^2-8x+3 =0
Delta = (-8)^2 -4(1)(3) = 52

Since Delta > 0
this equation has 2 Real solutions.

(By the way, since sqrt(Delta) is irrational, both solutions are also irrational.)

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