A-LevelMathematicsQuadratics9709/12 · Feb/Mar 2022 · Q25 Marks
A curve has equation y = x² + 2cx + 4 and a straight line has equation y = 4x + c, where c is a constant. Find the set of values of c for which the curve and line intersect at two distinct points.
- (a)Find the set of values of c for which the curve and line intersect at two distinct points.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [*M1] x² + 2cx + 4 = 4x + c leading to x²+2cx-4x+4-c [=0]
- [DM1] b²-4ac = (2c-4)²-4(4-c)
- [A1] [4c²-16c+16-16+4c=] 4c²-12c
- [M1] b² – 4ac > 0 leading to (4)c(c-3)> 0
- [A1] c<0, c>3
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