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

1 Answer
Gió
Feb 21, 2017

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

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