Question

If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)

Answer 1

If we write $k$ where we see $x$ in the equation and set the result equal to $-10$, we get the result.

• $f(k)=k(k)^3+k^2-k(k)+2$
• $=k^4+k^2-k^2+2$
• $=k^4+2=-10$
• $k^4=-12$
• $k_{1}=\sqrt[4]{3}(-1-i)$
• $k_{2}=\sqrt[4]{3}(-1+i)$
• $k_{3}=\sqrt[4]{3}(1-i)$
• $k_{4}=\sqrt[4]{3}(1+i)$