O-LevelAdditional MathematicsFactors of polynomials4037/12 · May/June 2011 · Q56 Marks
Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.
- (i)Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.[2]
- (ii)Hence show that 2x³ – 5x² + 10x − 4 = 0 has only one real root and state the value of this root.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- (i) 2(½)³ – 5(½)² + 10(½) – 4 = 0; M1 for substitution of x = 0.5 or at long division; A1
- (ii) (2x−1)(x²-2x+4); M1 attempt to obtain quadratic factor; A1 for correct quadratic factor
- For (x²-2x+4), b² < 4ac; M1 for correct use of discriminant or solution of quadratic equation = 0
- so only one real root of x = 0.5; A1, all correct with statement of root.
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