O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2020 · Q45 Marks
The three roots of p(x) = 0, where p(x) = 2x³ + ax² + bx + c are x = 1/2, x = n and x = −n, where a, b, c and n are integers. The y-intercept of the graph of y = p(x) is 4. Find p(x), simplifying your coefficients.
- (a)The three roots of p(x) = 0, where p(x) = 2x³ + ax² + bx + c are x = 1/2, x = n and x = −n, where a, b, c and n are integers. The y-intercept of the graph of y = p(x) is 4. Find p(x), simplifying your coefficients.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] Factorised form: (x+n)(x-n)(2x-1) oe
- [1] Multiplies out correctly
- [1] Correct expanded form in terms of n: 2x³ −x² −2n²x+n²
- [1] Uses (their n²) = 4 in their expression
- [1] 2x³-x²-8x+4
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