Master Writing the equation of a polynomial given irrational zeros

The video tutorial explains how to write polynomial equations when given irrational zeros. It covers methods such as using the square root to find zeros, applying the zero product property, and simplifying using the difference of squares. The tutorial also demonstrates complex polynomial multiplication using different methods, including the box method. The video concludes with a final example to reinforce the concepts discussed.

What is the result when you solve the equation X^2 = 3 using the square root method?

• X = ±3

• X = ±9

• X = ±sqrt(3)

• X = ±1.5

Why is it important to consider both positive and negative roots when given one irrational root?

• Because they are always equal

• To ensure all possible solutions are considered

• To avoid complex numbers

• To simplify the equation

What is the first step in writing the equation of a polynomial when given irrational zeros?

• Add the zeros

• Set the zeros equal to X

• Multiply the zeros

• Set the zeros equal to zero

What is the Zero Product Property used for in polynomial equations?

• To find the sum of the roots

• To set each factor equal to zero

• To multiply the factors

• To divide the polynomial

When multiplying polynomials, why is the box method preferred over FOIL?

• It is faster

• It is more accurate

• It is more visual and organized

• It requires fewer steps

What is the result of multiplying two conjugate binomials?

• A difference of squares

• A quotient of squares

• A product of squares

• A sum of squares

How do you handle complex irrational zeros in polynomial equations?

• By converting them to rational numbers

• By using only the positive root

• By using the distributive property and grouping

• By ignoring them

What is the purpose of grouping terms when dealing with complex irrational zeros?

• To create a difference of squares

• To add the terms

• To eliminate the zeros

• To simplify the equation

What is the final step in solving a polynomial equation with irrational zeros?

• Setting the equation to zero

• Dividing by the leading coefficient

• Replacing zero with F of X

• Adding all terms

What is the result of multiplying X^2 - 1 by X^2 - 4 using the box method?

• X^4 - 8X^2 + 16

• X^4 - 7X^2 + 12

• X^4 - 5X^2 + 4

• X^4 - 9X^2 + 20