Math Problem?

Question

I know I've seen this before but I just can't remember how to do it. y=x^3+2x+k where K is a constant and only has 1 x-intercept. Whats the solution.

Answer 1

only one x-intercept
means that
x^3+2x+k=0 has only one solution

Answer 2

What's the question? Normally, the solution is a graph. Each value of x creates a y value. Plot these on a graph. You'll see the value of k shifts the graph up or down. But regardless of what k is, there is only one x intercept.

Did you mean the graph intercepts the x-axis at x = 1? Then the solution is y = x^3 + 2x - 3

Answer 3

. I guess you want to determine k so that your polynomial has just 1 x intercept, that is, exactly one real root.T

he derivative of this polynomial is dy/dx = 3x^2 + 2, which is independent of k and positive for every real x. Therefore, y increases strictly with x along all the real line. Since y is a polynomial of odd degree, y -> -oo as x -> - oo and y -> oo as x -> oo. So, for every real k, the condition y =0 happens once and only once. In other words, for every real k, the polynomial has 1 and only 1 x intercept.

I hope I understood your question.

Answer 4

0=1+2+k
k=-3
Final equation will be
y=x^3+2x-3

I hope this helps!!