A QUADRATIC EQUATION AND ITS SOLUTION

QUADRATIC EQUATION
Any equation of the form ax²+bx+c=0 is called a quadratic equation where a, b, c are constants and a#0 ; x is a variable.
For any equation to be quadratic, x must be raised to the power 2.
Examples of quadratic equations include:
x²+5x+6=0
2y²-6y+12=0
3m²+m=0
p²-4=0.
You will realize that the variable in each of the equations is raised to the power 2; making each a quadratic equation.
Each has the same variable. This means an equation of the form 2x²+y-4=0 ,is not a quadratic equation. x and y are different variables.
SOLUTION OF A QUADRATIC EQUATION.
To solve a quadratic equation means to calculate the values of the variable that will make the equation equal to zero.
You can solve a quadratic equation by using the following methods ; factorization, completing the square, use of quadratic formula or graph.
Example: Solve the equation x²+5x+6=0
solution
x²+5x+6=0
factorization.
select any pair of factors of 6 in the equation whose sum is 5 the coefficient of x and whose product is 6.
factors of 6={1,2,3,6} or {-1,-2,-3,-6}.
from above 2+3=5, and 2x3=6. The numbers 2,3 are the factors of 6 that will be used to factorize and solve the equation as below:
x²+5x +6=0
(x+2)(x+3)=0 , since this product is zero, either (x+2)=0 or (x+3)=0.
solving the linear equations give x=-2, x=-3 as solutions to the equation x²+5x+6=0.