Zeros and Coefficients of a Polynomial

The video tutorial explains the concept of polynomial zeros, their geometric interpretation, and the relationship between zeros and coefficients for linear, quadratic, and cubic polynomials. It provides examples and proofs to illustrate these relationships and demonstrates how to form polynomials when zeros are given. The session also covers the maximum number of zeros a polynomial can have based on its degree.

What is the maximum number of zeros a cubic polynomial can have?

• 2

• 1

• 4

• 3

How is the zero of a linear polynomial determined?

• By the sum of the coefficients

• By the negative ratio of the constant term and the coefficient of the variable

• By the product of the coefficients

• By the square of the constant term

What is the sum of the zeros of the quadratic polynomial x^2 + 7x + 10?

• -10

• 10

• 7

• -7

What is the general formula for the sum of the zeros of a quadratic polynomial ax^2 + bx + c?

• -c/a

• c/a

• -b/a

• b/a

If the sum and product of zeros of a quadratic polynomial are given, what form does the polynomial take?

• k(x^2 - sum of zeros * x - product of zeros)

• k(x^2 + sum of zeros * x - product of zeros)

• k(x^2 - sum of zeros * x + product of zeros)

• k(x^2 + sum of zeros * x + product of zeros)

What is the sum of the zeros of a cubic polynomial ax^3 + bx^2 + cx + d?

• b/a

• -b/a

• c/a

• -c/a

For a cubic polynomial, what is the relationship between the product of the zeros and the coefficients?

• -d/a

• d/a

• c/a

• -c/a