Factorization using formula is explained in previous example (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:
\[x^2+4x+5=0\]
formula is given by
x=\[\frac{-b+/-\sqrt{b^2-4\times a\times c}}{2\times a}\]
given: a=1,b=4, c=5
substituting in formula
x =\[\frac{-4+/-\sqrt{4^2-4\times 1\times 5}}{2\times 1}\]
x= \[\frac{-4+/-\sqrt{16-20}}{2}\]
x= \[\frac{-4+/-\sqrt{-4}}{2}\]
x=\[\frac{-4+/-\sqrt{4\times -1}}{2}\]
but \[\sqrt{-1}\] = i (imaginary term)
x=\[\frac{-4+/-i\sqrt{4}}{2}\]
x=\[\frac{-4+/-2i}{2}\]
we shall find 2 values of x
when sign is +
x=\[\frac{-4+2i}{2}\]
x= \[-2+i\](taking 2 common in numerator and cancelling with denominator)
when sign is -
x=\[\frac{-4-2i}{2}\]
x=\[-2-i\] (taking 2 common in numerator and cancelling with denominator)
\[\therefore \] x= -2+i , -2-i
