SOLUTION: Use the given function to find all values of x that satisfy the inequality f(x) is greater than or equal to g(x). f(x)=5x^2 g(x)=19x-12 Select the correct shoice below and, i

Algebra ->  Inequalities -> SOLUTION: Use the given function to find all values of x that satisfy the inequality f(x) is greater than or equal to g(x). f(x)=5x^2 g(x)=19x-12 Select the correct shoice below and, i      Log On


   

Question 756693: Use the given function to find all values of x that satisfy the inequality f(x) is greater than or equal to g(x).
f(x)=5x^2
g(x)=19x-12
Select the correct shoice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ____. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
B. The solution set is 0.
Graph the solution set on a real number line.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!

f(x)>=g(x)
5%5E2%3E=19x-12
5x%5E2-19x%2B12%3E=0 THIS parabola has a minimum and opens upward. Know that this parabolas is different from the given parabola in the question.

Try first checking discriminant. Guess why?

%28-19%29%5E2-4%2A5%2A12=19%5E2-240=121 which is positive. We DO expect two roots.
x=%2819-sqrt%28121%29%29%2F%282%2A5%29=%2819-11%29%2F10=4%2F5
OR
x=%2819%2Bsqrt%28121%29%29%2F%282%2A5%29=%2819%2B11%29%2F10=3

Knowing how this parabola appears and having the x-intercepts, the original statement is true for x%3C=4%2F5 or for x%3E=3.

This intermediate parabola, not the originally given one:
graph%28300%2C300%2C-6%2C6%2C-9%2C9%2C5x%5E2-19x%2B12%29