How many, and what type of, solutions does y=x^2-8x+2 have?

2 nonreal solutions

1 rational solution

2 rational solutions

2 irrational solutions

The answer to your question is 2 rational solutions.

Step-by-step explanation:

Equation

y = x² - 8x + 2

Solve using the general formula

x = [8 ± √ (-8) ² - 4 (1) (2) ] / 2 (1)

Simplification

x = [8 ± √64 - 8] / 2

x = [8 ± √56] / 2

x = [8 ± 2√14]2

x₁ = 4 + √14 x₂ = 4 - √14

As √14 is positive, we conclude that the equation has two rational solutions.