Formula for solving quadratic equations

A quadratic functions in the variable of x is an equation of the general form ax^2 + b x + c = 0, Where a, b, c are real numbers, a not equal to Zero. 2x^2 + x – 300 = 0 is a quadratic equation.

The simplest way to solve ax2 + bx + c = 0 for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the given quadratic equation is too messy, or it doesn't factor at all. Factoring may not always be successful; the Quadratic Formula always helps to find the solution.

The Quadratic equation form is ax2 + bx + c, where a, b, and c are just numbers; they are known as the numerical coefficients. The Formula is derived by the process of completing the square.

That is, ax2+ bx + c = 0, a not equal to Zero, is called the standard form of a quadratic function


Formula for Solving Quadratic Equation:


The solutions of any quadratic equation, ax2 + bx + c = 0 is given by the following formula, called the formula of quadratic equation:

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

For using the Quadratic Formula to work, the equation must be re arranged in the form (quadratic) = 0. Also, the 2a in the denominator of the Formula is underneath everything above in the numerator, not just the square root. And there 2a  is under there, not just a plain 2.


solving quadratic equation - Example problems:


solving quadratic equation -  problem 1:

x2  + 9x + 8  = 0

Solution:

Factoring method is used to solve for x,

x2 + 1x + 8x + 8 = 0

x(x + 1) + 8(x + 1) = 0

(x + 1) ( x + 8 )=0

X = -1, -8

The answers are -1,-8.

solving quatratic equation -  Problem 2:

Solve: x2 + 8x + 12 = 0.

Solution:

Factoring method is used to solve for x,

x2 + 5x + 3x + 12=0

x(x+5) + 3(x + 4) =0

(x+5)(x+3)=0

x = - 5 , - 3

The answers are  -5, -3.

solving quatratic equation -  Problem 4:

Solve 3x2 + 5x = -1 for x.

Solution: First find the standard form of

The equations and determine a, b,and c.

2x2 + 6x + 1 = 0

a = 2

b = 6

c = 1

Plug the values you found for

a, b, and c into the

Quadratic formula.

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

Perform any indicated operations.

X = ` ( -6 +- sqrt(6^2 - 8))/(4) `

X = `(-6 +- sqrt (28)) / 4`

The solutions are as follows:


X =`(-6 + sqrt (28)) / 4`           and X =  `(-6 - sqrt (28)) / 4`