Question 952659: find all the real zeros of P(x), use the quadratic equation if necessary
P(x) = x^4-7x^3+14x^2-3x-9
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find all the real zeros of P(x), use the quadratic equation if necessary
P(x) = x^4-7x^3+14x^2-3x-9
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Use Rational Roots Theorem with synthetic division.
...0..|....1.....-7......14......-3......-9....
...1..|....1.....-6......8........5.......-4
...2..|....1.....-5......4........5........1 (real root between 1 & 2) (change of sign of last numbers)
...3..|....1.....-4......2........3........0 (3 is a root)
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...0..|....1.....-4......2........3.
...1..|....1.....-3.....-1........2
...2..|....1.....-2......2........7.
...3..|....1.....-1....-1........0 (3 is a root of mult. 2)
P(x)=(x-3)(x-3)(x^2-x-1)
zeros are: 3, 3, and two real irrational roots
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