Find The Four Real Zeros Of The Polynomial. f(x)= x^4+6x^3-15x^2-152x-240

Find The Four Real Zeros Of The Polynomial. f(x)= x^4+6x^3-15x^2-152x-240

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Descartes rule of signs tells us that there is only one positive root. Factoring theorem tells us that the rational roots would be factors 240 (which has many). To guess the positive root, seeing that the first two terms are positive, with small coefficients, and the remaining (negative) have large coefficients, we can try large factors, such as 4 (4^4=256), or 5 (5^4=625) by evaluating f(4) or f(5). Once we find the first one, the rest are negative roots of the remaining cubic.

so the anser would be -4,-4,-3,5 ?

Yes, how did you find them?

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