Quadratic equation is given by
a\[x^2\]+bx+c=0
we can find the value of 'x' using factorization using formula when factoring numbers is not possible.the formula is given by
x=\[\frac{-(b)+/-\sqrt{b^2-4\times a\times c}}{2\times a}\]
case 1: when \[b^2-4\times a\times c\] is positive
case 2: when \[b^2-4\times a\times c\] is negative (example will be given in further calculations)
example for case 1:
\[x^2-9x+20\]=0
x=\[\frac{-b+/-\sqrt{b^2-4\times a\times c}}{2\times a}\]
given a=1,b=-9,c=20
substituting in formula
x=\[\frac{-(-9)+/-\sqrt{-9^2-4\times 1\times 20}}{2\times 1}\]
x=\[\frac{9+/-\sqrt{81-80}}{2}\]
x=\[\frac{9+/-\sqrt{ 1}}{2}\ \]
x= \[\frac{9+/- 1}{2}\ \]
we shall find two values of x
when sign is +
x =\[\frac{9+1}{2}\ \] =5
when sign is -
x=\[\frac{9-1}{2}\ \] =4
\[\therefore \] x= 5,4
