Question:
Suppose the equation $x^3-hx^2+kx-9=0$ has only one real root which has a value of $1$. Find the range of values of $k$.
I really have no idea when it comes to a cubic equation. Any advice to solving?
[Math] Cubic Equation with one real root
cubics
Best Answer
You know that one factor of this cubic equation is $(x-1)$ from the root. Therefore, you can equate the above polynomial to $(x-1)(x^2 + ax +b)$ and use that to get the relationship between $h$ and $k$ on the one side and $a$ and $b$ on the other.
You also know that $(x^2 +ax +b)$ has no real roots. Using the discriminant should give you enough to finish the question.