1.3: Polynomial with a constant and no real solutions

0606/11/M/J/19 — Question 3 · 6 marks

The polynomial p(x)=(2x−1)(x+k)−12p(x) = (2x - 1)(x + k) - 12, where kk is a constant.
(i)
Write down the value of p(−k)p(-k).
[1]
(ii)
When p(x)p(x) is divided by x+3x + 3 the remainder is 23.
Find the value of kk.
[2]
(iii)
Using your value of kk, show that the equation p(x)=−25p(x) = -25 has no real solutions.
[3]