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

If `alpha,beta` are the roots of the equation `a x^2+b x+c=0,` then the value of `(aalpha^2+c)/(aalpha+b)+(abeta^2+c)/(abeta+b)` is a.`(b(b^2-2a c))/(4a)` b. `(b^2-4a c)/(2a)` c. `(b(b^2-2a c))/(a^2c)` d. none of these

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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