A-LevelMathematicsQuadratics9709/12 · May/June 2023 · Q33 Marks
Express 4x² – 24x + p in the form a(x + b)² + c, where a and b are integers and c is to be given in terms of the constant p.
- (a)Express 4x² – 24x + p in the form a(x + b)² + c, where a and b are integers and c is to be given in terms of the constant p.[2]
- (b)Hence or otherwise find the set of values of p for which the equation 4x² – 24x + p = 0 has no real roots.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [B1] 4(x-3)² seen or a = 4 and b = -3 OE Award marks for the correct expression or their values a, b and c. Condone 4(x-3) + p - 36 = 0 and 4(x - 9/4)^2
- [B1] -36+p or p-36 seen or c = p-36
- [B1] p-36>0 leading to p > 36 or 24² – 4×4p (0 => p) 36 or 36 < p Allow (36,∞) or 36 < p < ∞ . Consider final answer only.
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