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Consider the polynomial P(x)=−4x5+5x4−4x+5P(x)=−4x5+5x4−4x+5. (a) Verify that 12√(1+i)12(1+i) is a root of P(x)?(?). b) Given that...

Consider the polynomial P(x)=−4x5+5x4−4x+5P(x)=−4x5+5x4−4x+5.

(a) Verify that 12√(1+i)12(1+i) is a root of P(x)?(?).

b) Given that 12√(1+i)12(1+i) is also a root of P(−x)P(−x), without calculation list 44 distinct roots of P(x)P(x). Explain your answer.

(c) Prove that P(x)P(x) has no real roots in (−∞,0](−∞,0] or in [3,∞)[3,∞).

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