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If alpha, beta are the roots of the equa...

If `alpha, beta` are the roots of the equation `ax^(2) + bx + c = 0,` then the value of `(aalpha^(2) + c)/(aalpha + b)+(abeta^(2) + c)/(abeta + b)` is

A

`(b(b^(2) - 2ac))/(4a)`

B

`(b^(2) - 4ac)/(2a)`

C

`(b(b^(2) - 2ac))/(a^(2)c)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have `aalpha^(2) + c = -balpha` or `aalpha + b = -c/alpha`
Similarly, `abeta + b = -c/beta`
Hence, the given expression is
`b/c(alpha^(2) + beta^(2)) = (b(b^(2) - 2ac))/(a^(2)c)`
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