Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16$
A) zeros: $- 2 , - 1,1,2$
B) zeros: $- 4,4 , - 1,1$
C) zeros: $1,4$
D) zeros: $- 4 , - 1,1,0$
E) zeros: $- 1,1,2,16$

Question

Quizplus · Accepted Answer

To sketch the graph of the function, we can first factor it as follows:

$$P(x) = x^4 - 17x^2 + 16 = (x^2 - 16)(x^2 - 1) = (x-4)(x+4)(x-1)(x+1)$$

From this factorization, we can see that the zeros of the function are $x=-4, -1, 1, 4$. Therefore, the correct choice is B.

Sketch the Graph Of PPP To Find All Real Zeros P(x)=x4−17x2+16P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16P(x)=x4−17x2+16

Sketch the Graph Of $P$ To Find All Real Zeros $P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16$