Question

Find the discriminant and use it to determine if the solution has one real, two real, or two imaginary solutions.

1. x^ +4x+3=0

2. x^ -2x +1=0

3. -x^ -x =4

Answer 1

I will do #1, you'll do the rest.

x^2 + 4x + 3 = 0

The discriminant is the value of b^2 - 4ac

a= 1, b = 4, c = 3

so b^2 - 4ac = 16 - 4(1)(3) = 4

So the discrimiant is 4.

If the discrmiant is greater than zero and a perfect square...like 4 in our problem, then the roots are real and rational.
Done.

One note...if the discriminant is less than zero, like -12, the roots are imaginary

If the the discriminant is zero, roots are real and equal.

If the discrminnant is greater than zero but NOT a perfect square, then the roots are real, unequal, and irrational.

Answer 2

Now, you should be able to do #2 and #3 or any problem.