A-LevelMathematicsQuadratics9709/12 · May/June 2011 · Q35 Marks
The equation x² + px + q = 0, where p and q are constants, has roots –3 and 5.
- (i)Find the values of p and q.[2]
- (ii)Using these values of p and q, find the value of the constant r for which the equation x² + px + q + r = 0 has equal roots.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [2] (i) x² + px + q = (x+3)(x-5); M1 Must be (x+3) and (x-5); A1 co; → p = -2, q = -15. (any other method ok)
- [3] (ii) x² + px + q + r = 0; M1 Any use of “b² – 4ac”; DM1 c must include both q and r.; A1 co; Uses a, b and c correctly; r = 16; or (x+k)² → 2k = p (M1) k² = q+r (M1) → k = -1 → r = 16 (A1)
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