Polynomials | SFALXO

Core Concepts

For a quadratic polynomial ax² + bx + c, if its zeroes are α and β:

α + β = -b / a

αβ = c / a

For a cubic polynomial ax³ + bx² + cx + d, if its zeroes are α, β, and γ:

α + β + γ = -b / a

αβ + βγ + γα = c / a

αβγ = -d / a

The number of zeroes of a polynomial is equal to the number of points where its graph intersects or touches the x-axis.

A quadratic polynomial graph is a parabola and may have 0, 1, or 2 real zeroes.

Forming a Quadratic Polynomial: If zeroes α and β are given, the quadratic polynomial is given by: x² - (α + β)x + αβ.

Degree & Zeroes: A polynomial of degree n can have at most n real zeroes.

Find the zeroes of 2x² - 7x + 3 and verify the relationship between the zeroes and the coefficients.
Form a quadratic polynomial whose zeroes are 3 and -5.
Find the value of k if one zero of kx² - 14x + 8 is twice the other.

α + β = -coefficient of x / coefficient of x²

αβ = constant term / coefficient of x²

Zeroes are the x-coordinates of points where y = p(x) intersects the x-axis.

A polynomial of degree n has at most n zeroes.