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.
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