A partial solution set is given for the equation. $$x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } + 84 x - 126 = 0 ; \{ 3,3 \}$$
Find the complete solution set.
A) $\quad 3,3 , \sqrt { 17 } , - \sqrt { 17 }$
B) $\quad 7,7 , \sqrt { 14 } , - \sqrt { 14 }$
C) $3,3 , \sqrt { 7 } , - \sqrt { 7 }$
D) $\quad 3,3 , \sqrt { 14 } , - \sqrt { 14 }$
E) none of these

Question

Quizplus · Accepted Answer

The given polynomial has a double root at $x = 3$. By factoring out $(x-3)^2$, the remaining quadratic can be solved to find the other roots, which are $\sqrt{14}$ and $-\sqrt{14}$.

A Partial Solution Set Is Given for the Equation x4−6x3−5x2+84x−126=0;{3,3}x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } + 84 x - 126 = 0 ; \{ 3,3 \}x4−6x3−5x2+84x−126=0;{3,3}

A Partial Solution Set Is Given for the Equation $x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } + 84 x - 126 = 0 ; \{ 3,3 \}$