Math CentralQuandaries & Queries


Question from peter, a student:

How do you find the roots of an equation without graphing? like, i have a problem that says what is the sum of the roots of x^4-x^3+5x^2+4=0.

Hi Peter,

Suppose the roots are a, b, c and d then you know that

x4 - x3 + 5x2 + 4 = (x - a)(x - b)(x - c)(x - d)

Expand the right side and you will get a polynomial of the form

x4 - x3 + 5x2 + 4 = (x - a)(x - b)(x - c)(x - d) = Px4 + Qx3 + Rx2 + Sx + T

Where P, Q, R and S are expressions involving a, b, c and d. Examine P, Q, R, S and T. What do they tell you about a + b + c + d?


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