Question

What are the zeros of(x²−4)(x⁴−16)?

a) x= −2,−1,1,2
b) x= −4,−2,2,4
c) x= −3, −1,1,3
d) x= −4,−3,3,4

Answer 1

The zeros of the function (x²−4)(x⁴−16) are x = −2 and x = 2. This is because both factors (x²−4) and (x⁴−16), when set to zero, lead to these solutions. Answer choice b) x = −4,−2,2,4 is therefore correct.

Step-by-step explanation:

The student is asking for the zeros of the function (x²−4)(x⁴−16). To find the zeros, we can set each factor equal to zero and solve for x.

For the first factor (x²−4), this gives us x² = 4. We can solve this by taking the square root of both sides, yielding x = ±2, which gives us two zeros at x = 2 and x = -2.

The second factor (x⁴−16) is equivalent to (x²−4)(x²+4). We already know that x²−4 gives us the zeros at x = ±2. However, x²+4 cannot be factored using real numbers and therefore does not contribute any real zeros to the function.

Overall, the zeros of the given function are x = -2, and x = 2. Hence, the correct answer is b) x = −4,−2,2,4.