Use the Rational Zero Theorem to create a list of all possible rational zeroes of the function f left parenthesis x right parenthesis equals 14 x superscript 7 baseline minus 4 x squared plus 2.
(1 point)
Responses
plus or minus 1 comma plus or minus 2 comma plus or minus one half comma plus or minus Start Fraction 1 over 7 End Fraction comma plus or minus Start Fraction 1 over 14 End Fraction comma plus or minus Start Fraction 2 over 7 End Fraction
plus or minus 1 comma plus or minus 2 comma plus or minus 7 comma plus or minus 14 comma plus or minus Start Fraction 7 over 2 End Fraction
plus or minus 1 comma plus or minus 2 comma plus or minus 7 comma plus or minus 14
plus or minus 1 comma plus or minus 2 comma plus or minus Start Fraction 1 over 7 End Fraction comma plus or minus Start Fraction 1 over 14 End Fraction
The possible rational zeroes can be found using the Rational Zero Theorem, which states that if a polynomial function has a rational zero, it must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
For the given function f(x) = 14x^7 - 4x^2 + 2, the leading coefficient is 14 and the constant term is 2. Therefore, the possible rational zeroes are of the form p/q, where p is a factor of 2 and q is a factor of 14.
The factors of 2 are 1 and 2, and the factors of 14 are 1, 2, 7, and 14. Combined with their negatives, the possible rational zeroes are:
±1, ±2, ±1/2, ±1/7, ±1/14, ±2/7
Therefore, the correct answer is:
plus or minus 1, plus or minus 2, plus or minus one half, plus or minus 1/7, plus or minus 1/14, plus or minus 2/7