How to write the equation of a polynomial given irrational zeros

The video tutorial covers the concept of conjugates in algebra, emphasizing the importance of recognizing both positive and negative square roots. It demonstrates solving equations using conjugates and introduces the box method for multiplying trinomials. The tutorial also explains the difference of two squares technique, providing a shortcut for simplifying complex expressions. The lesson concludes with a final solution, preparing students for similar problems on a quiz.

What must you remember when you encounter a positive square root in an equation?

• Use only the complex conjugate.

• Only the positive root is needed.

• The negative root should also be considered.

• Ignore the root entirely.

When solving equations with conjugates, what method can help simplify the multiplication process?

• The subtraction method

• The box method

• The addition method

• The division method

What is the result of multiplying (X - 1) by itself?

• X^2 - 2X + 1

• X^2 + 2X + 1

• X^2 - 1

• X^2 + 1

In the difference of squares method, what happens to the middle terms?

• They remain unchanged.

• They are multiplied.

• They cancel each other out.

• They are added together.

What is the final polynomial expression obtained in the video?

• Y = X^3 - 5X^2 + 5X + 3

• Y = X^3 + 3X^2 - 3X - 5

• Y = X^3 + 5X^2 - 5X - 3

• Y = X^3 - 3X^2 + 3X + 5