SOLUTION: For about what value(s) of x does g(x) = k(x) if g(x) = x^3 + 2x^2 and k(x) = x^3 – x^2 + 6?
a. x = ± 2.3
b. x ≈ 2.3
c. x ≈ ± 1.4
d. x ≈ 1.4
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Question 152870: For about what value(s) of x does g(x) = k(x) if g(x) = x^3 + 2x^2 and k(x) = x^3 – x^2 + 6?
a. x = ± 2.3
b. x ≈ 2.3
c. x ≈ ± 1.4
d. x ≈ 1.4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.
Plug in and
Subtract from both sides. Subtract from both sides.
Notice we have a quadratic equation in the form of where , , and
Let's use the quadratic formula to solve for x
Start with the quadratic formula
Plug in , , and
Square to get .
Multiply to get
Rewrite as
Add to to get
Multiply and to get .
Simplify the square root (note: If you need help with simplifying square roots, check out this solver)
Break up the fraction.
Reduce.
or Break up the expression.
So the answers are or
which approximate to or
So the answer choice is c) x ≈ ± 1.4
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