Question

Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x^2 + 5x

A. Double root
B. Real and rational roots
C. Real and irrational roots
D. Non-real roots

Answer 1

If the discriminate is equal to 0, then there is one real root multiplicity 2; if the discriminate is >0, then there are 2 real and rational roots; if the discriminate is <0, there are no-real roots because you can't take the square root of a negative number and get real roots. Our discriminate is found by subbing into the quadratic formula and taking into consideration ONLY what is under the radical. Ours is
`√(5^2-4(1)(-2))=√(25+8)=√(33)`. That is a positive 33, so the discriminate is >0 but not a perfect square, so our answer is that there are 2 real and rational zeros or solutions or roots. They all mean the same thing.