find all zeros of h(x)=7x^4+3x^3-2x^2-x+1

Question

it relates to roots and zeros

Answer 1

We need a value of x which makes h(x) negative and another that makes it positive. When this happens, there will be a root between the two values of x. We can put x=0 so h(0)=1. h(1)=8, which is bigger than 1. That seems to be the wrong direction. What about h(-1)? That's 4, which is bigger than 1. Try h(0.5)=7/16+3/8-1/2-1/2+1=13/16, which is smaller than 1. That's better. Try h(-0.5)=7/16-3/8-1/2+1/2+1=17/16, bigger than 1.

However, this function doesn't drop below about 0.6383 when x=0.3575, so that precludes real roots.

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