Question

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Answer 1

Finding the Discriminant of a function will tell you what kind of solutions it will have. Do you know how to do that?

Answer 2

b^2 - 4ac is your Discriminant formula

Answer 3

If the Discriminant is a positive perfect square, you will have two real solutions. If it is zero, you'll have 1 real solution. If it is positive then 2 irrational solutions and if it's negative then 2 complex solutions.

Answer 4

So x^2 + 2x + 2 will give you 2 complex solutions.

Answer 5

Therefore x^2 + 2x + 2 is your answer for h(x)

Answer 6

Eyeball problems. Just write them down.

• One function, f(x), with two real rational solutions.

f(x) = (x)(x-2) -- Done!

• One function, g(x), with two real irrational solution

g(x) = (x + sqrt(3))(x - sqrt(3)) -- Done!

• One function, h(x), with two complex solutions.

h(x) = x^2 + 1 -- Done!

You may wish to multiply them out and put them in some unfactored form.