Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$
A) zeros: $- 2 , - 1,1,2$
B) zeros: $- 4 , - 1$
C) zeros: $1,2$
D) zeros: $- 2 , - 1,1,0$
E) zeros: $- 1,0,2$

Question

Quizplus · Accepted Answer

We can factor $P(x)$ as $P(x)=(x^2-4)(x^2-1)$. The zeros are the values of $x$ that make $P(x)=0$. Therefore, we need to solve the equations $(x^2-4)(x^2-1)=0$. Factoring each factor again, we get $(x-2)(x+2)(x-1)(x+1)=0$. Setting each factor equal to zero and solving for $x$, we get the zeros to be $-2, -1, 1,$ and $2$. Therefore, the answer is choice A.

Sketch the Graph Of PPP To Find All Real Zeros P(x)=x4−5x2+4P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4P(x)=x4−5x2+4

Sketch the Graph Of $P$ To Find All Real Zeros $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$