Find all rational zeros.
-$$f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18$$
A) 6,1
B) $- 6,1$
C) No rational zeros
D) $6 , - 1$

Question

Quizplus · Accepted Answer

The rational root theorem can be used to find the rational zeros of the polynomial. The possible rational zeros are the factors of the constant term (-18) divided by the factors of the leading coefficient (1). The factors of -18 are ±1, ±2, ±3, ±6, ±9, ±18. Testing these values, we find that 6 and 1 are zeros of the polynomial.

Find All Rational Zeros f(x)=x4−7x3+3x2+21x−18f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18f(x)=x4−7x3+3x2+21x−18

Find All Rational Zeros $f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18$