Problem 90 - Algebra and Trigonometry

Question

Find all values of \(x\) satisfying the given conditions. $$y=x^{3}+4 x^{2}-x+6 \text { and } y=10$$

Step-by-Step Solution

Answer

The solutions for \(x\) can be found by a numerical solver.

Step 1: Set up the equation

We start off by setting the two given functions equal to each other: \(x^{3}+4 x^{2}-x+6 = 10\). This results in a cubic equation as this: \(x^{3}+4x^{2}-x-4=0\)

Step 2: Apply a root-finding method

We can use a numerical solver as the cubic root finding method in this case is non-trivial. If you put the equation into a solver, it will find the roots for \(x\).

Step 3: Interpret the results

The solutions for \(x\) provided by the solver will be the numbers that make the original equation true. Thus, these are the values of \(x\) that satisfy the given conditions.