If `alpha and beta "are the roots of the quadratic equation" ax^(2) +bx+c=0`, then
`lim_(xrarr(1)/(alpha)sqrt(1-(cos ex^(2) + bx +a)/(2(1-alphax)^(2)))=`

Options

A. `|(c )/(2alpha)((1)/(alpha)-(1)/(beta))|`
B. `|(c )/(2beta)((1)/(alpha)-(1)/(beta))|`
C. `|(c )/(2beta)((1)/(alpha)-(1)/(beta))|`
D. None of these

Answer

1

Explanation

`ax^(2)+bx+c rarr roots are alpha,beta`
`cx^(2) + bx + a rarr "roots are" (1)/(alpha), (1)/(beta)`
`underset(xrarrl//alpha)limsqrt(1-cos c(x-1//alpha)(x-1//beta).C^(2)(x-1//beta)^(2))/(2a^(2)(x-1//alpha)a^(2)(x-1//beta)^(2))c^(2)`
`=underset(xrarr//a)limsqrt((1)/(2).(1)/(2alpha^(2))c^(2)(x-1//beta))^(2)`
`1/2.|c/alpha|1/alpha-1/beta|`