Finding the polynomial when given imaginary zeros - Online Math Tutor

The video tutorial covers the concept of conjugate pairs in complex numbers, explaining how they are used to rationalize complex numbers and find polynomial zeros. It demonstrates the process of converting zeros to factors and introduces the box method for multiplying binomials. The tutorial concludes with constructing a final polynomial expression, emphasizing the importance of understanding complex zeros and their conjugates.

What is the conjugate of the complex number 1 + 5i?

• -1 + 5i

• 1 - 5i

• -1 - 5i

• 1 + 5i

If 1 - i is a zero of a polynomial, what is another zero?

• 1 + i

• -1 + i

• -1 - i

• 1 - i

What is the first step in converting zeros to polynomial factors?

• Subtract the zeros

• Multiply the zeros

• Add the zeros

• Express zeros as factors

What is the purpose of the box method in multiplication?

• To simplify addition

• To solve equations

• To organize terms and avoid errors

• To divide polynomials

What is the result of multiplying x + 5i and x - 5i using the box method?

• x^2 - 10xi

• x^2 + 25

• x^2 + 10xi

• x^2 - 25

What is the final polynomial expression obtained in the video?

• x^3 - x^2 - 25x + 25

• x^3 - x^2 + 25x - 25

• x^3 + x^2 - 25x - 25

• x^3 + x^2 + 25x + 25

Why does the i squared term change the sign in the polynomial?

• Because i squared is positive

• Because i squared is negative

• Because i squared is imaginary

• Because i squared is zero