Find all the rational zeros of the function.
$x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$
A) $- 5$
B) $0 , - 1$
C) 0,5
D) 5
E) $\pm 5$

Question

Find all the rational zeros of the function. 
$x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$
A) $- 5$
B) $0 , - 1$
C) 0,5
D) 5
E) $\pm 5$

Quizplus · Accepted Answer

The rational zeros of a polynomial can be found using the Rational Root Theorem, which suggests that any rational root, in the form of a fraction p/q, is a divisor of the constant term (in this case, -125) divided by a divisor of the leading coefficient (in this case, 1). For this polynomial, the possible rational roots are divisors of -125, which are ±1, ±5, ±25, ±125. Testing these values or using synthetic division, we find that 5 is a root because substituting x = 5 into the polynomial gives 0. None of the other options are roots of the polynomial.

Find All the Rational Zeros of the Function x3−15x2+75x−125x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125x3−15x2+75x−125

Find All the Rational Zeros of the Function $x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$