The given function is f = 4x^4 - 101x^2 + 25.

To find the zeros of the function, we first set the function equal to zero and solve for x:

4x^4 - 101x^2 + 25 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where x^2 is considered as a single variable.

Let's substitute y = x^2. The equation becomes:

4y^2 - 101y + 25 = 0

Now, we can solve this quadratic equation using the quadratic formula y = [-b ± sqrt(b^2 - 4ac)] / (2a):

y = [101 ± sqrt((-101)^2 - 4*4*25)] / (2*4)
y = [101 ± sqrt(10201 - 400)] / 8
y = [101 ± sqrt(9801)] / 8
y = [101 ± 99] / 8

So, the solutions for y are y1 = 25 and y2 = 0.25.

Remember that y = x^2, so to find the zeros of the function, we need to solve for x:

x^2 = 25 = x = ±5
x^2 = 0.25 = x = ±0.5

So, the zeros of the function are -5, -0.5, 0.5, and 5. Each zero appears only once in the function, so each has a multiplicity of 1.

Therefore, the correct answer is d. -5, -0.5, 0.5, 5; each of multiplicity 1.

Question

The given function is f = 4x^4 - 101x^2 + 25.

To find the zeros of the function, we first set the function equal to zero and solve for x:

4x^4 - 101x^2 + 25 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where x^2 is considered as a single variable.

Let's substitute y = x^2. The equation becomes:

4y^2 - 101y + 25 = 0

Now, we can solve this quadratic equation using the quadratic formula y = [-b ± sqrt(b^2 - 4ac)] / (2a):

y = [101 ± sqrt((-101)^2 - 4*4*25)] / (2*4)
y = [101 ± sqrt(10201 - 400)] / 8
y = [101 ± sqrt(9801)] / 8
y = [101 ± 99] / 8

So, the solutions for y are y1 = 25 and y2 = 0.25.

Remember that y = x^2, so to find the zeros of the function, we need to solve for x:

x^2 = 25 => x = ±5
x^2 = 0.25 => x = ±0.5

So, the zeros of the function are -5, -0.5, 0.5, and 5. Each zero appears only once in the function, so each has a multiplicity of 1.

Therefore, the correct answer is d. -5, -0.5, 0.5, 5; each of multiplicity 1.

Knowee AI · Accepted Answer