book Maths Puzzle Numerical Ability

List all of the potential rational zeros of the polynomial function. Do not attempt to find the zeros.

f(x)=5x^3+2x^2-2x+5

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book Other Question

P(x)=2x^2-3x^2+4x-5

The P(1)=-2
P(2)=7 and
P(-1)=?
If a,b,c are in Arithmetic progression and a^2,b^2,c^2 are in Harmonic progression then what is the relation connecting a,b,c?