A-LevelMathematicsAlgebra9709/32 · Oct/Nov 2022 · Q26 Marks
The polynomial 2x³ – x² + a, where a is a constant, is denoted by p(x). It is given that (2x + 3) is a factor of p(x).
- (a)Find the value of a.[2]
- (b)When a has this value, solve the inequality p(x) < 0.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [M1] (a) Substitute x = -3/2 and equate result to zero
- [A1] (a) Obtain a = 9
- [*M1] (b) Commence division by (2x+3) reaching a partial quotient x² + kx
- [A1] (b) Obtain factorisation (2x+3)(x²-2x+3)
- [DM1] (b) Show that x² – 2x + 3 is always positive, or 2x³ – x² +9 only intersects the x-axis once
- [A1] (b) State final answer x < -3/2 from correct work
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