Use the discriminate to determine the number and the nature of the solutions of the giving equation

2x^2 + 5x+7=0

Since b^2 - 4ac = - 31 we have 2 complex roots

Step-by-step explanation:

2x^2 + 5x+7=0

The discriminant is b^2 - 4ac

when the equation is ax^2 + bx+c

so a = 2 b=5 and c=7

(5) ^2 - 4 (2) (7)

25 - 56

-31

If b^2 - 4ac > 0 we have 2 real distinct roots

If b^2 - 4ac = 0 we have one real root

If b^2 - 4ac < 0 we have two complex root

Since b^2 - 4ac = - 31 we have 2 complex roots