$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$
A) 1,-1,7
B) $- \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$
C) 2,-2,7
D) $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$

Question

$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$
A)  1,-1,7 
B) $- \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$
C)  2,-2,7 
D) $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$

Quizplus · Accepted Answer

The correct roots can be found by factoring or using the rational root theorem and synthetic division. The given polynomial doesn't factor easily, so we test possible rational roots derived from the factors of the constant term and the leading coefficient. The correct roots are $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$, which satisfy the equation when substituted back into it.

4x3−28x2−x+7=04 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 04x3−28x2−x+7=0

$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$