SOLUTION: Find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.)       Log On


   

Question 626379: Find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.)

P(x) = x5 − 9x4 + 34x3 − 58x2 + 45x − 13
Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
P(x) = x5 − 9x4 + 34x3 − 58x2 + 45x − 13
Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
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Use rational roots theorem to solve:
...0...|....1.......-9........34......-58......45.......-13
...1...|....1.......-8........26......-32......13.........0 (1 is a zero)
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...0...|....1.......-8....... 26......-32......13..
...1...|....1.......-7........19......-13.......0 (1 is a zero again)
=======================
...0...|....1.......-7........19.......-13...........
...1...|....1.......-6........13.........0 (1 is a zero a third time)
P(x)=(x-1)(x-1)(x-1)(x^2-6x+13)
zeros are: 1,1,1, and 2 non real roots