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
Feb 21, 2017

Answer:

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#