9709 P22 - Jun 2025 - Q5 - 9 marks
9408
The polynomial \(p(x)\) is defined by \[p(x)=ax^4+bx^3+13x^2-35x+15,\] where \(a\) and \(b\) are constants. It is given that \((2x-1)\) and \((x-3)\) are factors of \(p(x)\).
(a) Find the values of \(a\) and \(b\). [4]
(b) Hence factorise \(p(x)\). [3]
(c) Find the least positive value of \(\theta\) in radians such that \(p(\cot2\theta)=0\). [2]
