Question

Determine the number of real solutions of x2 + 5x + 8 = 0

Answer 1

Use the discriminant from the quadratic formula:\[x = \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a }\]This is for equations in the form:\[ax ^{2} + bx + c = 0\]The discriminant is:\[\sqrt{b ^{2} - 4ac}\]Just use that last part and see if that is negative or not. First identify "a", "b", and "c".

Answer 2

\[x ^{2} + 5x + 8 = 0\]is the same as:\[(1)x ^{2} + (5)x + (8) = 0\]so, a = 1, b = 5, and c = 8

Answer 3

Are you all set now or would you like the next steps?

Answer 4

\[\sqrt{5^{2} - (4)(1)(8)} = \sqrt{25 - 32} = \sqrt{-7}\]But since what is under the radical is negative, there are no real solutions.

Answer 5

Good luck to you in all of your studies, and nice working with you! @Stephensparadox