# math

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staright line y=x-1 meets curve
y=x^2-5x-8 at the points A and B.
the curve y=p+qx-2x^2 also passes through ponts A and B. what are the values of p and q??

• math -

First, find the intersection of y = x-1 with y = x^2 - 5x - 8
that is, solve
x^2 - 5x - 8 = x - 1
x^2 - 6x - 7 = 0
(x-7)(x+1) = 0
x = -7 or x = -1
sub that back into y = x-1 to get
y = 6 or y = -2 respectively
so we have A(7,6) and B(-1,-2)

since these two points also lie on ty = p + qx - 2x^2 let's sub them in

6 = p + 6q - 98 and
-2 = p -q - 8

re-arrange these two equations and solve.
They are easy to solve as it by subtracting them, since the p's are the same.

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