Statement 1: The quadratic polynomial `y=ax^(2)+bx+c(a!=0` and `a,b in R)` is symmetric about the line `2ax+b=0`
Statement 2: Parabola is symmetric about its axis of symmetry.

Options

A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1
B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true

Answer

A

Explanation

Statement is is obviously true.
Burt `y=ax^(2)+bx+c`
`y=a(x^(2)+b/ax+c/a)`
`=a{(x+b/(2a)^(2)-D/(4a^(2))}` [ where `D=b^(2)-4ac`]
`implies(x+b/(2a))^(2)=1/a(y+D/(4a))`
Let `x+b/(2a)=X` and `y=D/(4a)=Y`
`:.X^(2)=1/aY`
Equation of axis `X=0` i.e. `x+b/(2a)=0`
or `2ax+b=0`
Hence `y=ax^(3)+bx+c` is symmetric about the lien `2ax+b=0`
`:.` Both statements are true and Statement 2 is a correct explanation of Statement -1.