數學，求solution，同polynomials有關

Let f(x) = -px^2+2x+5.

f(c) = a represents the remainder is equal to a when f(x) is divided by x-c.

When x = 2,
f(x) = -p(2)^2 + 2(2) + 5
= -4p + 9

When x = -1/2,
f(x) = -p(-1/2)^2 + 2(-1/2) + 5
= -1/4 p + 4

Now, the remainders are equal.
So, -4p + 9 = - 1/4 p + 4
4p - 1/4 p = 9 - 4
15/4 p = 5
p = 4/3

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