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Find the zeros of the function:

\[ f(x) = 4x^4 - 4x^3 - 25x^2 + x + 25 \]

Answer :

Final answer:

To find the zeros of the function f(x) = 4x^4 - 4x^3 - 25x^2 + x + 25, you can use the quadratic formula. The zeros are approximately x = -0.601, x = 1.587, x = -0.675 ± 3.497i (where i is the imaginary unit).

Explanation:

To find the zeros of the function f(x) = 4x^4 - 4x^3 - 25x^2 + x + 25, we need to solve the equation 4x^4 - 4x^3 - 25x^2 + x + 25 = 0. There are different methods to solve this equation, but one common approach is to use factoring and the quadratic formula.

Step 1: Factor the equation (if possible)

In this case, the equation cannot be easily factored, so we move on to the next step.

Step 2: Use the quadratic formula

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). By comparing the equation 4x^4 - 4x^3 - 25x^2 + x + 25 = 0 to the general form ax^2 + bx + c = 0, we can determine that a = 4, b = -4, and c = 25.

Now we can substitute these values into the quadratic formula and solve for x.

Step 3: Solve for x

Using the quadratic formula, we find that the zeros of the function are approximately x = -0.601, x = 1.587, x = -0.675 ± 3.497i, where i is the imaginary unit.

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