Question 452448: The function below has at least one rational zero.
Use this fact to find all zeros of the function.
f(x)=7x^4 +27x^3 -40x^2 +x +5
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The function below has at least one rational zero.
Use this fact to find all zeros of the function.
f(x)=7x^4 +27x^3 -40x^2 +x +5
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The sum of the coefficients is zero, so x = 1 is a zero.
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Use synthetic division to find other zeroes:
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1)....7....27....-40....1....5
.......7.....34.....-6...-5...|..0
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The quotient, 7x^3+34x^2-6x+5 has a zero
at x = -5, which I found using
a graphing calculator.
-5).......7.....34.....-6...-5
...........7.....-1.....-1...|..0
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Use the quadratic formula to find the zeroes
of 7x^2-x-1 = 0
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Cheers,
Stan H.
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