Question

How many real solutions does the equation 5x^2 + 8x - 1 = 0

Answer 1

2 real solutions

Explanation:

Currently, this quadratic equation is in standard form, which is:

`ax^2+bx+c=0`

We can find the number of real solutions using the discriminant from the quadratic equation which is:

`b^2-4ac`

When b^2 - 4ac > 0, there are 2 real solutions

When b^2 - 4ac = 0, there is 1 real solution

When b^2 - 4ac < 0, there are 0 real solutions

In the example, our a value is 5, our b value is 8 and our c value is -1:

`8^2-4(5)(-1)\\64-20=44`

44 > 0, so there are 2 real solutions