Question

Describe the variable methods for finding the solutions of a quadratic.

Answer 1

quadratic equation is of the form

y = ax^2 + bx + c

quadratic equation can be solved by 3 methods

1) ac factoring

2) quadratic formula

3) completing squares

in ac factoring method we find two factors of a*c such that they add up to become mid term 'b'

for example : y = x^2 + 5x + 6

factors of a*c that is 6 is 2 and 3

so we can write the equation as

( x + 2) (x+3 ) = 0

x = -2 , x = -3

in 2nd method quadratic formula

we have a standard formula for finding solution

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

a = 1 , b = 5 , c = 6

plugging the values

x = [ -5 +- sqrt ( 25 - 16 ) ] / 2

x = -2 , -3