A-LevelMathematicsAlgebra9709/22 · Oct/Nov 2022 · Q47 Marks
The polynomial p(x) is defined by p(x) = ax³ + 23x² - ax – 8, where a is a constant. It is given that (2x + 1) is a factor of p(x).
- (a)Find the value of a and hence factorise p(x) completely.[5]
- (b)Hence solve the equation p(e4y) = 0, giving your answer correct to 3 significant figures.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [M1] Substitute x = −½, equate to zero and attempt solution
- [A1] Obtain a = 6
- [M1] Divide by 2x + 1 at least as far as the x term or use of identity or by inspection.
- [A1] Obtain 3x² + 10x − 8
- [A1] Conclude (2x + 1)(3x − 2)(x + 4)
- [M1] Apply logarithms and use power law for e^(4y) = k where k > 0 Using their answer to (a).
- [A1] Obtain y = −0.101 and no other answers or greater accuracy.
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