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Let alpha and beta be the distinct roots...

Let `alpha` and `beta` be the distinct roots of `ax^(2) + bx + c = 0` then `underset(x to alpha)(Lt) (1 - cos (ax^(2) + bx + c))/((x - alpha)^(2))` equal to

A

`( a^(2))/( 2) ( alpha - beta )^(2)`

B

0

C

` (- a^(2))/( 2) ( alpha - beta )^(2)`

D

`(1)/(2) ( alpha - beta)^(2)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If alpha and beta are the roots of equation ax^2 + bx + c = 0, then the value of alpha/beta + beta/alpha is

    A
    `(b^2 - 2ac)/(ac)`
    B
    `(b^2 - ac)/(ac)`
    C
    `(c^2 - 2ab)/(ab)`
    D
    `(c^2 -a^2)/(ab)`

  • If alpha and beta are the roots of ax^(2)+bx+c=0 , then the value of (a alpha +b)^(-2)+ (a beta +b)^(-2) is equal to

    A
    `(b^(2)-2ac)/(a^(2)c^(2))`
    B
    `(c^(2)-2ab)/(a^(2)b^(2))`
    C
    `(a^(2)-2bc)/(b^(2)c^(2))`
    D
    none

  • If alpha and beta are the roots of the equation ax ^(2) + bx + c = 0, then (1 + alpha + alpha ^(2)) (1 + beta + beta ^(2)) is equal to

    A
    0
    B
    positive
    C
    negative
    D
    None

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