math
posted by tommas .
staright line y=x1 meets curve
y=x^25x8 at the points A and B.
the curve y=p+qx2x^2 also passes through ponts A and B. what are the values of p and q??
helpppppplease...thanks

First, find the intersection of y = x1 with y = x^2  5x  8
that is, solve
x^2  5x  8 = x  1
x^2  6x  7 = 0
(x7)(x+1) = 0
x = 7 or x = 1
sub that back into y = x1 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
rearrange these two equations and solve.
They are easy to solve as it by subtracting them, since the p's are the same.