1. How many real solutions does the quadratic equation x?+9x= -8 have?

This quadratic equation has 2 solutions.

Step-by-step explanation:

I assume the '?' in your question is meant to be power 2 (²), or else it would not be a quadratic equation. You could write it using the superscript version of 2.

We can solve this equation by expressing it in the form: ax² + bx + c

x² + 9x= -8

x² + 9x + 8 = 0

Now if you know the discriminant, you can simply plug in your values of a, b, and c to see how many solutions there are.

In this case, you would not need the discriminant as there are whole-number factors and hence this can simply be factorised.

x² + 9x + 8 = 0

(x + 8)(x + 1) = 0

For this equation to be true (= 0), x can equal -8 OR -1.

Hence, this quadratic equation has 2 solutions.