Writing the equation of a polynomial given a complex root

👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Also recall that when a complex/imaginary number is a zero to a polynomial, the conjugate of the complex/imaginary number will also be a zero to the polynomial.

To write the equation of a polynomial, we write the given zeros in factor form and expand the product of the factors. Thus, given a, b, . . . as zeros to a polynomial, we write the equation of the polynomial by expanding the factors (x - a)(x - b) . . . = 0

Organized Videos:
✅Write the Equation of a Polynomial Given the Zeros
✅Write the Equation of a Polynomial Given Complex Zeros
✅Write the Equation of a Polynomial Given Zeros with Fractions
✅Write the Equation of a Polynomial Given Real Zeros
✅Write the Equation of a Polynomial Given Irrational Zeros
✅Write the Equation of a Polynomial Given Imaginary Zeros
✅Write the Equation of a Polynomial Given Zeros | Learn About

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This is how I started:   (X+2)(X-3)(X-Zi)(X+Zi) = Y
after simplifying I got:
(X^2-X-6)(X^2+Z^2) = Y
I plugged in the point (1, 5)
Z^2 = sq rt of 11/16 i

Am I even close?