How To Solve Quadratic Equations
Quadratic Equation is a polynomial equation of second degree. The general form of a how to solve quadratic equations
is ax2+bx+c = 0.
The contributions of the ancient Indian Mathematicians to quadratic equations are quite significant and
extensive. Before 800BC Indian Mathematicians constructed 'altars' based on the solutions of quadratic
equation ax2+bx+c =0, Aryabhatta gave a rule to sum the geometric series which involves the solution of a
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Formation of a Quadratic Equation
Let us form the quadratic equation
whose roots are
[alpha] and [beta] .
Then x = [alpha] , y = [beta] are the roots
Therefore x - [alpha] = 0 and
, y - [beta=0]
so (x - [alpha] ) (y - [beta] [)= 0]
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Maximum and Minimum Values of a Quadratic Expression
An expression of the type ax2+bx+c is called " quadratic expression".
The quadratic expression ax2+bx+c takes different values as x takes different values.
As x varies from - [prop] to + [prop] ax2+bx+c
1. has a minimum value whenever a> 0.
The minimum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = - b/2a.
2. has a maximum value whenever a< 0.
The maximum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = - b/2a.
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