A-LevelMathematicsAlgebra9709/22 · May/June 2020 · Q68 Marks
The polynomial p(x) is defined by p(x) = 6x³ + ax² - 4x – 3, where a is a constant. It is given that (x + 3) is a factor of p(x).
- (a)Find the value of a.[2]
- (b)Using this value of a, factorise p(x) completely.[3]
- (c)Hence solve the equation p(cosec θ) = 0 for 0° < θ < 360°.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] Substitute x = -3, equate to zero and attempt solution for a
- [A1] Obtain a = 17
- [M1] Divide by x + 3 at least as far as the x term
- [A1] Obtain 6x^2 - x - 1
- [A1] Conclude (x + 3)(3x+1)(2x-1)
- [M1] Attempt solution of sin θ = k where -1 ≤ k ≤ 1
- [A1] Obtain 199.5
- [A1] Obtain 340.5
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