Mathguru – Help – Finding a quadratic polynomial whose zeroes are given.

Solved Example > No. SE 5

Finding a quadratic polynomial whose zeroes are given.

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Explanation:

In mathematics, a quadratic polynomial or quadratic is a polynomial of degree two, also called second-order polynomial. That means the exponents of the polynomial's variables are no larger than 2. For example, x² − 4x + 7 is a quadratic polynomial, while x³ − 4x + 7 is not.

http://en.wikipedia.org/wiki/Quadratic_polynomial

A quadratic function, in mathematics, is a polynomial function of the form

$f(x)=ax^2+bx+c,\quad a \ne 0.$

The expression $ax$ $2$ $+$ $bx$ $+$ $c$ in the definition of a quadratic function is a polynomial of degree 2 or second order, or a 2nd degree polynomial, because the highest exponent of x is 2.

If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the equation.

Roots

The roots (zeros) of the quadratic function

$f(x) = ax^2+bx+c\,$

are the values of x for which f(x) = 0. (Our solved example in mathguru.com uses this concept).

When the coefficients a, b, and c, are real or complex, the roots are

$x=\frac{-b \pm \sqrt{\Delta}}{2 a},$

where the discriminant is defined as

$\Delta = b^2 - 4 a c \, .$

http://en.wikipedia.org/wiki/Quadratic_function

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License