यदि `ax^(2)+bx+c=a(x-p)^(2)` है तो `a,b,c` का संबंध क्या होगा?

Options

A. `abc=1`
B. `b^(2)=ac`
C. `b^(2)=4ac`
D. `2b=a+c`

Answer

C

Explanation

`ax^(2)+bx+c=a(x-p)^(2)`
`ax^(2)+bx+c=a(x^(2)+p^(2)-2px)`
`impliesax^(2)+bx+c=ax^(2)+ap^(2)-2apx`
Comparing coefficient of `x^(2)` and `x`
`implies b=-2ap`
`impliesp=(-b)/(2a)`………..i
an `c=ap^(2)`
`impliesc=axx(b^(2))/(4a^(2))` (From (i))
`4ac=b^(2)`