Polynomials

Chapter 2

What is a linear polynomial?

• A polynomial of degree one

What is a quadratic polynomial?

• A polynomial of degree two

What is a cubic polynomial?

• A polynomial of degree three

In what circumstance are parabolas formed?

• A quadratic polynomial ax² + bx + c, a isn’t = 0 the graph of the corresponding equation y = ax² + bx + c has one of the two shapes of a Parabola

Two shapes of a parabola?

• One thats open upwards

• One thats open downwards

What factor decides the shape of the parabolas?

• Depending on whether

  • a > 0

  • a < 0

General form of a quadratic polynomial

• ax² + bx + c

• ‘a’ , ‘b’ and ‘c’ are real numbers

• ‘a’ is not = 0

What is the maximum amount of zeroes a quadratic polynomial can have? What about cubic?

• 2 for quadratic

• 3 for cubic

Sum of roots of a quadratic polynomial

• α + β = -b/a

• α and β are the zeroes

Product of roots of a quadratic polynomial

• α × β = c/a

• α and β are the zeroes

Sum of roots of a cubic polynomial

• α + β + γ = -b/a

• α, β and γ are the zeroes

Sum of product of roots of a cubic polynomial

• αβ + βγ + γα = c/a

• α, β and γ are the zeroes

Product of roots of a cubic polynomial

• αβγ = -d/a

• α, β and γ are the zeroes