63.0k views
2 votes
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.

1 Answer

4 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 Jacob Franklin
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories