C1 2016 8 Edexcel

8

a) we want to find a constraint thats means there are no solutions to the equation
3x-7=2px^{2}-6px+4p
0=2px^{2}-x(6p+3)+(4p+7)
The determinant of this function must be less than 0 for us to have no real solutions
\therefore (6p+3)^2 -4(4p+7)2p<0
36p^2+36p+9-32p^2-56p<0
4p^2-20p+9<0

b) 4p^2-20p+9=(2p-9)(2p-1)
\therefore 4p^2-20p+9<0 for 0.5<p<4.5

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