Find the real solutions of the polynomial equation. $q ^ { 4 } - 17 q ^ { 2 } + 16 = 0$
A) $1,16$
B) $1 , - 4$
C) $\pm 1 , \pm 16$
D) $\pm 1 , \pm 4$
E) $- 1,16$

Question

Quizplus · Accepted Answer

This equation can be solved by substituting $p = q^2$, turning it into a quadratic equation $p^2 - 17p + 16 = 0$. Solving this gives $p = 1$ and $p = 16$, which means $q^2 = 1$ and $q^2 = 16$. Therefore, the real solutions for $q$ are $\pm 1$ and $\pm 4$.

Find the Real Solutions of the Polynomial Equation q4−17q2+16=0q ^ { 4 } - 17 q ^ { 2 } + 16 = 0q4−17q2+16=0

Find the Real Solutions of the Polynomial Equation $q ^ { 4 } - 17 q ^ { 2 } + 16 = 0$