Relationship Between Zeroes and Coefficients of a Polynomial

The video tutorial explores the relationship between the zeroes and coefficients of polynomials, covering linear, quadratic, and cubic types. It explains how to find zeroes by equating polynomials to zero and factorizing them. The session delves into the sum and product of zeroes, establishing relationships for quadratic and cubic polynomials. It also demonstrates solving problems using these relationships, emphasizing the importance of choosing the simplest form for polynomials.

What is the first step in finding the zeroes of a polynomial?

• Equate the polynomial to 1

• Equate the polynomial to 0

• Multiply the polynomial by its coefficients

• Divide the polynomial by its highest degree term

What is the general form of a linear polynomial?

• ax + b

• x + b

• ax^3 + bx^2 + cx + d

• ax^2 + bx + c

For a linear polynomial, the relationship between zeroes and coefficients is given by:

• a/b

• -b/a

• b/a

• -a/b

In a quadratic polynomial, the sum of the zeroes is related to which coefficients?

• Coefficient of x and x^2

• Coefficient of x^2 and constant term

• Coefficient of x and constant term

• Coefficient of x^2 and x^3

What is the product of the zeroes for a quadratic polynomial?

• c/a

• -c/a

• -b/a

• b/a

When given the sum and product of zeroes, what is the assumed value of 'a' for simplicity?

• 0

• 1

• 2

• 5

If the sum of zeroes is 8 and the product is 12, what is the quadratic polynomial?

• x^2 - 8x + 12

• x^2 + 8x - 12

• x^2 - 8x - 12

• x^2 + 8x + 12