Write the equation of the polynomial given the zeros

👉 Learn how to write the equation of a polynomial when given irrational 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 the square root of a number (irrational zero) is a zero to a polynomial, the conjugate of the irrational zero 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

Timestamps:
0:00 Intro
0:25 Start of Problem

Corrections:
2:54 It was supposed to be -5x. The final polynomial should be x^3 - 4x^2 - 5x + 20

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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[digantraval]

i think it's supposed to be -5x, the final poly should be x^3 - 4x^2 - 5x + 20

[hannahtitialii]

ummm... isn't it supposed to be -5x???

[danielbowino]

There is an error in the answer. It is supposed to be X^3- 4x^2-5x + 20=0

[ryn]

Hi - How did you get -5x^2 (to then be -9x^2)?  Wouldn't it be just -5x?