Polynomial Formula

Introduction for polynomial formula:

In this article we see how to factor a quadratic equation or polynomial equation using a polynomial formula. Quadratic equation consists of x^2,x terms with constants, x^2 and x coefficient are taken as 'a' and 'b', then constant as c. we can substitute the values in the quadratic formula and we solve it to get the factors of the quadratic equation. Let us see some example problems for polynomial formula.

Polynomial Formula:

Formula:

Quadratic equation is a polynomial equation and it is second order.

ax^2 + bx + c = 0 let this is a quadratic equation

The formula for factoring quadratic equationis

x =`(-b+-sqrt(b^2 - 4ac))/(2a)`

Let us see some example problems for solving the factorization using polynomial formula. Is this topic how many sides does a polygon have hard for you? Watch out for my coming posts.

Examples for Polynomial Formula:

Example1:

Solve the quadratic equation x^2 - 5x +6 = 0

Solution:

Given: a = 1, b = -5 and c = 6

x =`(-b+-sqrt(b^2 - 4ac))/(2a)`

x =`(-(-5)+-sqrt(-5^2 - 4(1)(6)))/(2xx1)`


x =   `(5+-sqrt(25-24))/(2)`

x = `(5+- sqrt(1))/2 `

x = `(5+1)/2` and x = `(5-1)/2`

x =3 and x = 2


Therefore factors of 2x^2 + x -1 =0 is x =3 and x = 2


Example2:

Factor the quadratic equation x^2 +2 x -3 = 0

Solution:

Given: a = 1, b = 2 and c = -3

x =`(-b+-sqrt(b^2 - 4ac))/(2a)`

x =`(-2+-sqrt(2^2 - 4(1)(-3)))/(2xx1)`


x =   `(-2+-sqrt(4+12))/(2)`

x = `(-2+- 4)/2 `

x = `(-2+4)/2` and x = `(-2-4)/2`

x = 1   and x = -3

Therefore factors of x^2 + 2x -3 =0 is x =1 and x = -3

Example2:

Factor the quadratic equation x^2 + 4x +2 = 0

Solution:

Given: a = 1, b = 4 and c = 2

x =`(-b+-sqrt(b^2 - 4ac))/(2a)`

x =`(-4+-sqrt(4^2 - 4(1)(2)))/(2xx1)`


x =   `(-4+-sqrt(16-8))/(2)`

x = `(-4+- 2sqrt(2))/2 `

x = `(-4+2sqrt(2))/2` and x = `(-4-2sqrt(2))/2`

x = -2 + √2   and x = -2-√2

Therefore factors of x^2 + 4x +2 =0 is   x = -2 + √2   and x = -2-√2