Question

How do you find the discriminant and how many solutions does `x^2 + 2x – 2 = 0` have?

Answer 1

For an equation in the general form:
`ax^2+bx+c=0`
the discriminant is:
`Delta = b^2 - 4ac`
and
`Delta { (<0 rarr "no Real solutions"), (=0 rarr "1 Real solution"), (>0 rarr "2 Real solutions"):}`

For `x^2+2x-2 = 0`
`Delta = (2)^2 - 4(1)(-2) = 12 >0`
so this equation has 2 Real solutions

Answer 2

Your equation is in the form: `ax^2+bx+c=0`
Where:
`a=1`
`b=2`
`c=-2`
The discriminant is:
`Delta=b^2-4ac=4-4(1*-2)=4+8=12>0`
Now, if:
1] `Delta>0` you have 2 distinct Real solutions;
2] `Delta=0` you have two Real coincident solutions;
3] `Delta<0` you have no Real solutions.