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| Math Central | Quandaries & Queries |
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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?
Harley
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