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Consider the following.f(x) = -2x4 + 13x3 – 21x2 + 2x + 8(a) List the possible rational zeros of f. (Enter your answers as a comma-separated list.

User Karim Samir
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1 Answer

20 votes
20 votes

\operatorname{\pm}1,\operatorname{\pm}(1)/(2),\operatorname{\pm}2,\operatorname{\pm}4,\operatorname{\pm}8

1) We need to use the Rational Roots Theorem:


f\mleft(x\mright)=-2x^4+13x^3-21x^2+2x+8

So, let's write out a ratio with the possible rational roots, considering the constant term and the leading coefficient:


(constant\:term\:divisors)/(leading\:coefficient\:divisors)=(\pm1,2,4,8)/(\pm1,2)

a) So the list of all possible zeros is:


\pm1,\pm(1)/(2),\pm2,\pm4,\pm8

Note that "possible' does not mean the list of all real rational roots. We'd need to plug into the function and check

User Inetknght
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