SOLUTION: Consider f(x) = 3x^4 - 11x^3 + 10x - 4; use the Rational Zero Theorem to find a zero. a. x = 0 b. x = 1 c. x = -5 d. x = -1 The constant term is -4 and the leading coe

Algebra ->  Equations -> SOLUTION: Consider f(x) = 3x^4 - 11x^3 + 10x - 4; use the Rational Zero Theorem to find a zero. a. x = 0 b. x = 1 c. x = -5 d. x = -1 The constant term is -4 and the leading coe      Log On


   

Question 144118: Consider f(x) = 3x^4 - 11x^3 + 10x - 4; use the Rational Zero Theorem to find a zero.
a. x = 0
b. x = 1
c. x = -5
d. x = -1
The constant term is -4 and the leading coefficient is 3. Then
constant term: 1, -1, 2, -2, 4, -4
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leading coefficient: 1, -1, 2, -2, 4, -4, 1/3, -1/3, 2/3, -2/3, 4/3, -4/3
There is no solution set???? Help
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You have identified all of the possible rational zeros. Only 2 of them are represented in your set of answers, so you only have to check those two. Remember that if a is a zero, then f%28a%29=0

f%28x%29+=+3x%5E4+-+11x%5E3+%2B+10x+-+4
f%281%29+=+3%281%29%5E4+-+11%281%29%5E3+%2B+10%281%29+-+4=3-11%2B10-4=-2. Therefore not a zero
f%28-1%29+=+3%28-1%29%5E4+-+11%28-1%29%5E3+%2B+10%28-1%29+-+4=3%2B11-10-4=0. Therefore -1 is a zero.

Answer d.

Super Double Plus Extra Credit:
Are there any other rational zeros? Hint: Use polynomial long division or synthetic division to divide f%28x%29 by x%2B1. Remember to include 0x%5E2 as a place holder. Repeat use of the Rational Zero Theorem to find any zeros for the 3rd degree polynomial quotient.