SOLUTION: Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x2 + 5x double root real and rational root real and irrational root imag

Algebra ->  Equations -> SOLUTION: Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x2 + 5x double root real and rational root real and irrational root imag      Log On


   

Question 1039805: Use the discriminant to describe the roots of each equation. Then select the best description.
2 = x2 + 5x
double root
real and rational root
real and irrational root
imaginary root
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+x%5E2+%2B+5x+
The discriminant is:
+b%5E2+-+4%2Aa%2Ac+
The general equation for a quadratic has the form:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+1+
+b+=+5+
+c+=+0+
+b%5E2+-+4%2Aa%2Ac+=+5%5E2+-+4%2A1%2A0+
+b%5E2+-+4%2Aa%2Ac+=+25+
---------------------
The discriminant is real and positive, and it is not zero
also, the discriminant is a perfect square. When you
plug the discriminant back into the quadratic
formula, you have 2 real, rational roots
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
---------------------
Here's the plot of the equation:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+5x+%29+