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Monica [59]
2 years ago
10

Find the polynomial function in standard form that has the zeros listed. i and -i

Mathematics
1 answer:
fgiga [73]2 years ago
7 0

The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

<h3>What is polynomial function?</h3>

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

  • The sum of the roots = (- coefficient of x)/(coefficient of x²)

         x1 + x2 = (-b)/a

  • The multiplication of the roots = constant/coefficient of x²

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

To know more about Polynomial Function, here

brainly.com/question/10918240

#SPJ4

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