A-LevelMathematicsAlgebra9709/22 · Feb/Mar 2023 · Q38 Marks
The polynomial p(x) is defined by p(x) = ax³ – ax² + ax + b, where a and b are constants. It is given that (x + 2) is a factor of p(x), and that the remainder is 35 when p(x) is divided by (x – 3).
- (a)Find the values of a and b.[5]
- (b)Hence factorise p(x) and show that the equation p(x) = 0 has exactly one real root.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.
- [M1] (a) Substitute x=-2 and equate to zero
- [M1] (a) Substitute x=3 and equate to 35
- [A1] (a) Obtain -8a-4a-2a+b=0 and 27a-9a+3a+b=35
- [DM1] (a) Solve a pair of relevant simultaneous linear equations to find a or b Dependent at least one M mark.
- [A1] (a) Obtain a=1 and b=14
- [M1] (b) Divide by x+2 at least as far as the x term
- [A1] (b) Obtain [(x+2)](x² -3x+7)
- [A1] (b) Conclude with reference to -2, and discriminant is 9-28 and hence no root OE
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →