SOLUTION: Consider the functions f(x) = 2x + 25, g(x) = x2 + 5, and h(x) = 5x. At what integer value of x does the quadratic function, g(x), begin to exceed the linear function, f(x)?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Consider the functions f(x) = 2x + 25, g(x) = x2 + 5, and h(x) = 5x. At what integer value of x does the quadratic function, g(x), begin to exceed the linear function, f(x)?      Log On


   

Question 968648: Consider the functions f(x) = 2x + 25, g(x) = x2 + 5, and h(x) = 5x.

At what integer value of x does the quadratic function, g(x), begin to exceed the linear function, f(x)?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B5%3E2x%2B25
x%5E2-2x-20%3E0

g exceeds f for any values to the left of the lesser root of this inequality, and to the right of the greater root of this inequality.

ROOTS:

%282%2B-+sqrt%284%2B4%2A20%29%29%2F2
%282%2B-+2%2Asqrt%281%2B20%29%29%2F2
highlight_green%281%2B-+sqrt%2821%29%29, only the roots for the described inequality.

This is not the final answer, because you want to know the integer values; but you can be sure that no values between the roots satisfy the inequality.