The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
How If `a and b`are rational and b is not perfect square, then the quadratic equaiton with rational coefficients whose one root is `3a + sqrt(b)` is

Options

A. `x^(2) - 6ax + 9a^(2) - b=0`
B. `3ax^(2) + x-sqrt(b) = 0`
C. `x^(2) + 3 x + sqrt(b) =0`
D. `sqrt(b)x^(2) + x- 3a = 0`

Answer

A

Explanation

Since b is not a perfect square, therefore other root will be `3a -sqrt(b))`
Required quadratic equation is
`x^(2) - [ (3a + sqrt(b))+(3a - sqrt(b))]x + (3a+sqrt(b))(3a - sqrt(b)) =0 `
`rArr x^(2) - 6ax + 9a^(2) - b =0`