Question

How do use the discriminant to find all values of c for which the equation `2x^2+5x+c=0` has two real roots?

Answer 1

I tried this:

Explanation:

We need the discriminant to be greater then zero to have two different real roots (if it is equal to zero you'll have two coincident real roots). So we need:

`Delta=b^2-4ac>0`

where we use the convention for the general form of our equation where:
`ax^2+bx+c=0`

we get:

`Delta=5^2-4(2c)>0`
`25-8c>0`

rearranging:

`8c<25`
and
`c<25/8`

You can test your result by setting:

`c=25/8`
it'll give you `Delta=0`

`c=25/8-1`
it'll give you `Delta=8`

`c=25/8+1`
it'll give you `Delta=-8`