core 1

Write down the set of values of the constant k for which equation 2x^3 -3x^2 -12x-7 = k has exactly one real solution.( 2 marks)

Working out :
2x^3 -3x^2 -12x-7 = (x+1)^2 (2x-7)
how do find the set of values from which k has exactly one real solution from this^?

Write down the set of values of the constant k for which equation 2x^3 -3x^2 -12x-7 = k has exactly one real solution.( 2 marks)

Working out :
2x^3 -3x^2 -12x-7 = (x+1)^2 (2x-7)
how do find the set of values from which k has exactly one real solution from this^?

If you have the graph, and worked out the stationary points, (and I assume you have these, since this is only 2 marks) then it should be obvious that it's any $k$ above the local maximum, or below the local minimum.

What you said about the k being above the local maximum.. works to give me the correct answer but can i just ask why the y value of the stationary point is used instead of the x value?

Because $2x^3 -3x^2 -12x-7 = k$ denotes the intersection between $y=2x^3 -3x^2 -12x-7$ and $y=k$. So when we say "For what values of $k$..." we are basically asking "For what values of y..."