The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
If the roots of a quadratic equation are `m+n and m-n`, then the quadratic equaiton will be :

Options

A. `x^(2) + 2 mx + m^(2) - mn + n^(2) = 0`
B. `x^(2) + 2 mx + ( m-n)^(2)= 0`
C. `x^(2) + 2 mx + m^(2) - n^(2) =0`
D. `x^(2) mx+ m^(2) - n^(2) =0`

Answer

C

Explanation

Let ` alpha = m+n , beta = m-n`
Now, `alpha + beta = m+n + m-n = 2 m`
`alpha xx beta = ( m+n) (m-n) = m^(2) - n^(2).`
Now, Required Quadratic Equation will be,
`x^(2) - ( alpha + beta) x + alpha beta = 0`
`alpha xx beta = (m+n) ( m-n) = m^(2) - n^(2)`.
Now, Required Quadratic Equaiton will be,
`x^(2) - ( alpha + beta) x + alpha beta = 0`
`x^(2) - 2m x + m^(2) - n^(2) = 0`