Question

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.
a. ) x2 + 6x - 7 = 0
b. ) z2 + z + 1 = 0
c. ) (3)1/2y2 - 4y - 7(3)1/2 = 0
d. ) 2x2 - 10x + 25 = 0

Answer 1

I really just do not understand what they are asking me to do here. I get useing the discriminat part but the just determine the number and types of solutions is whats geting me

Answer 2

the discriminant is
\[b^2-4ac\] and they are asking you just to compute this

Answer 3

for for example in the first one
\[b^2-4ac=6^2-4\times 1\times (-7)=36+28=64\]
that means there are two solutions, and since 64 is a perfect square it means the solutions are rational

Answer 4

in the second one
\[b^2-4ac=1^2-4\times 1\times 1=-3\] which is negative. two complex solutions