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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29+=+k%28x%29+ Start with the given equation.


x%5E3+%2B+2x%5E2=+x%5E3+-+x%5E2+%2B+6 Plug in g%28x%29+=+x%5E3+%2B+2x%5E2 and k%28x%29+=+x%5E3+-+x%5E2+%2B+6


0=++-+3x%5E2+%2B+6 Subtract x%5E3 from both sides. Subtract 2x%5E2 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-3, b=0, and c=6


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%28-3%29%286%29+%29%29%2F%282%28-3%29%29 Plug in a=-3, b=0, and c=6


x+=+%280+%2B-+sqrt%28+0-4%28-3%29%286%29+%29%29%2F%282%28-3%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--72+%29%29%2F%282%28-3%29%29 Multiply 4%28-3%29%286%29 to get -72


x+=+%280+%2B-+sqrt%28+0%2B72+%29%29%2F%282%28-3%29%29 Rewrite sqrt%280--72%29 as sqrt%280%2B72%29


x+=+%280+%2B-+sqrt%28+72+%29%29%2F%282%28-3%29%29 Add 0 to 72 to get 72


x+=+%280+%2B-+sqrt%28+72+%29%29%2F%28-6%29 Multiply 2 and -3 to get -6.


x+=+%280+%2B-+6%2Asqrt%282%29%29%2F%28-6%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%280%29%2F%28-6%29+%2B-+%286%2Asqrt%282%29%29%2F%28-6%29 Break up the fraction.


x+=+0+%2B-+-1%2Asqrt%282%29 Reduce.


x+=+0-1%2Asqrt%282%29 or x+=+0%2B1%2Asqrt%282%29 Break up the expression.


So the answers are x+=+0-1%2Asqrt%282%29 or x+=+0%2B1%2Asqrt%282%29


which approximate to x=-1.414 or x=1.414

So the answer choice is c) x ≈ ± 1.4