use the discriminant to determine the number and type of solutions

Question

3a^2+2a=5

-4p^2+8p=7

Answer 1

b²-4ac is the discriminant

3a²+2a-5=0

4-4(3)(-5)=4+60=64 (2 different real roots)

b²-4ac > 0 means 2 different real roots

b²-4ac < 0 means 2 complex roots

-4p²+8p=7

4p²-8p+7=0

64-4(4)(7)=64-112=-48 (2 complex roots)