Question

How to use the discriminant to find out how many real number roots an equation has for `14a^2 - a= 5a^2 - 5a`?

Answer 1

Write it collecting all terms to the left as in:
`14a^2-a-5a^2+5a=0`
`9a^2+4a=0`

This is in the form:
`ma^2+na+p=0`
where:
`m=9`
`n=4`
`p=0`
The discriminant is:
`Delta=n^2-4mp=16-4(9*0)=16>0`
Your equation will give you 2 real distict solutions.
[In this case `x_1=0 and x_2=-4/9`]