Find all the real zeros of $f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 5$ .
A) $x = \frac { 5 } { 4 } , - \frac { 4 } { 5 }$
B) $x = 4,1 , - 5$
C) $x = \pm 1 , \frac { 5 } { 4 }$
D) $x = \frac { 5 } { 4 }$
E) $x = \frac { 1 } { 4 } , - \frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

To find the real zeros of the polynomial $f(x) = 4x^3 - 5x^2 + 4x - 5$, one can use methods such as factoring, synthetic division, or the Rational Root Theorem. However, without performing these calculations explicitly, it's not straightforward to directly identify the zeros. Given the options, the correct answer can be verified by substituting the values back into the polynomial. Only $x = \frac{5}{4}$ satisfies the equation $4x^3 - 5x^2 + 4x - 5 = 0$, making it the correct choice. The other options either do not satisfy the equation or represent multiple roots not applicable to this polynomial.

Find All the Real Zeros Of f(x)=4x3−5x2+4x−5f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 5f(x)=4x3−5x2+4x−5

Find All the Real Zeros Of $f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 5$