In the given figure, vertices of `Delta ABC` lie on `y = f(x) = ax^2 + bx + c.` The `DeltaABC` is right angled isosceles triangle whose hypotenuse `AC = 4sqrt2` units. Number of integral values of `k` for which one root of `f(x) = 0` is more than `k` and other less than `k`

Options

A. `y = x^(2) - 2sqrt(2)`
B. `y = x^(2) - 12`
C. `y = (x^(2))/(2)-2`
D. `y = (x^(2))/(2sqrt(2)) - 2 sqrt(2)`

Answer

4

Explanation

`because AC = 4sqrt(2)`
`therefore AB = BC = (4sqrt(2))/(2) =4` units
`OB = sqrt(4^(2) -(2sqrt(2))^(2)) = 2sqrt(2)`
`therefore A(-2sqrt(2),0),C(2sqrt(2),0),B(0,-2sqrt(2))`
Since `y = ax^(2) + bx + x` passes through A,B and C, we get
`y = (x^(2))/(2sqrt(2)) - 2sqrt(2)`