A-LevelMathematicsAlgebra9709/22 · May/June 2018 · Q36 Marks
Find the quotient when x⁴ – 2x³ + 8x² – 12x + 13 is divided by x² + 6 and show that the remainder is 1.
- (i)Find the quotient when x⁴ – 2x³ + 8x² – 12x + 13 is divided by x² + 6 and show that the remainder is 1.[3]
- (ii)Show that the equation x⁴ – 2x³ + 8x² – 12x + 12 = 0 has no real roots.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] Carry out division and reach at least partial quotient of form x² + kx
- [A1] Obtain quotient x² – 2x + 2
- [A1] AG; necessary detail needed and all correct Obtain remainder 1
- [B1] FT State equation as (x² + 6)(x² – 2x + 2) = 0 Following their 3-term quotient from part (i)
- [M1] Calculate discriminant of 3-term quadratic or equivalent
- [A1] AG; necessary detail needed Obtain -4 and state no root, also referring to no root from x² +6 factor
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