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)`