The perfect square form of the quadratic equation `ax^(2)+bx+c=0(ane0)` is

Options

A. `(x+(b)/(2a))^(2)=(b^(2)-4ac)/(4a^(2))`
B. `(x-(b)/(2a))^(2)=( b^(2)-4ac)/(4a^(2))`
C. `(x+(b)/(2a))^(2)=( b^(2)-4ac)/(4a)`
D. `(x-(b)/(2a))^(2)=( b^(2)-4ac)/(2a)`

Explanation

Given that `ax^(2)+bx+c=0(ane0)`
or, `x^(2)+(b)/(a)+(c)/(a)=0`
or, `x^(2)+2.x(b)/(2a)+((b)/(2a))^(2)+(c)/(a)=((b)/(2a))^(2)`
or, `(x+(b)/(2a))^(2)=(b^(2))/(4a^(2))-(c)/(a)`
or, `(x+(b)/(2a))=(b^(2)-4ac)/(4a^(2))`
Hence the required perfect square form is `(x+(b)/(2a))=(b^(2)-4ac)/(4a^(2))`