Question

Find the zeros of each function if h(x) has zeros at x1, x2, and x3. C(x) = 7h(x)

A) Zeros of C(x) = {7x1, 7x2, 7x3}
B) Zeros of C(x) = {x1 + x2 + x3}
C) Zeros of C(x) = {x1/7, x2/7, x3/7}
D) Zeros of C(x) = {x1⁷, x2⁷, x3⁷}

Answer 1

The zeros of C(x), when C(x) = 7h(x) and h(x) has zeros at x1, x2, and x3, remain the same: {x1, x2, x3}, since multiplying by a constant does not change the location of zeros.

Step-by-step explanation:

To find the zeros of the function C(x) given that C(x) = 7h(x) and h(x) has zeros at x1, x2, and x3, we need to think about what happens when we multiply the function by a constant. Multiplying h(x) by 7 does not change the locations of its zeros, it only changes the value of the function at every point by a factor of 7. Therefore, the zeros of C(x) remain at x1, x2, and x3. This is because if h(x1) = 0, then 7 × h(x1) = 7 × 0 = 0, and similarly for x2 and x3. Hence, the correct answer is:

Zeros of C(x) = {x1, x2, x3}