# How do you know how many solutions #2x^2+5x-7=0# has?

##### 2 Answers

The roots are

graph{2x^2+5x-7 [-20, 20, -12,12] [-20, 20, -12, 12]}

#### Explanation:

One way to find the number of roots is by the graph. It is clear that the graph crosses the x-axis at 2 different values of x. Therefore there are 2 roots.

graph{2x^2+5x-7 [-20, 20, -12,12] [-20, 20, -12, 12]}

The give equation is

By factoring method,

by the zero property

it follows

the roots are

It can also be checked from the graph the points

God bless...I hope the explanation is useful.

Using the quadratic formula, you can find out that the quadratic has two real solutions.

#### Explanation:

By evaluating the discriminant from the quadratic formula (

If the discriminant is greater than

Furthermore, if the discriminant is greater than

If the discriminant is exactly

Lastly, if the discriminant is less than

Let's evaluate the discriminant for our quadratic:

Since the discriminant is greater than