Question

What is the value of the one real solution for y = x^3 - x^2 + 5

Answer 1

Answer:

$x=-1.433$

Explanation:

The easier way to solve this problem is to graph the function using graphing calculator. Here we have the following function:

$y=f(x)= x^3 - x^2 + 5$

So this is a cubic function that extends to $\infty$ as x tends to $\infty$ and $-\infty$ as x tends to $-\infty$. This is so because the leading coefficient (the coefficient that accompanies $x^3$) is positive. Then, this graph will pass through a point in the x-axis which is the value of the only real solution. The graph shows that this value is:

$x=-1.433$