SOLUTION: use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; jus

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; jus      Log On


   

Question 36031: use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions.
x^2 + 6x - 7 = 0
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to know what the discriminant is.
It is the portion underneath the root in the quadratic formula.
x+=+%28-b+%2B-+highlight%28sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%29%2F%282%2Aa%29+
so now using the equation you have ...
+x%5E2+%2B+6x+-+7+=+0+
+b%5E2+-+4%2Aa%2Ac+
Plug in the values
+6%5E2+-+4%2A1%2A%28-7%29+
+36+-+4%2A1%2A%28-7%29+
+36+%2B+28+
+64+
because this number is positive, there are 2 roots.
if the number were 0, there would be one root.
if the number was negative, there are no roots.