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If f(x) = x^{4}+ 2x^{3}+ 5x^{2}- 16x - 20, show that f(x) can be expressed in the form (x^{2}+ x +a)^{2}- 4(x +b)^{2}, where a and b are constant to be determined.

Hence, or otherwise, find both the real roots of the eqaution f(x) = 0. Find also the set of values of x such that f(x) > 0.

I tried completing the square

but i found

(x^{2}+ x + (4x+30)/8)^{2}- 4[(x^{2})/16 + 4x + 185/32]

my a and b is WAY too off the answer, which is a = 4 and b = 3. Any help?

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# Homework Help: Completing the square problem

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