If `alpha,beta` are the roots of the equation `a x^2+b x+c=0`, then `1/(aalpha+b)+1/(abeta+b)=`

Options

A. `c/(ab)`
B. `a/(bc)`
C. `b/(ac)`
D. none of these

Answer

B

Explanation

`alpha,beta`
are the roots of the equation `ax^2+bx+c=0`

Sum of roots`=alpha+beta= −b/a`

And product of roots `=alphabeta= c/a`

Now,

`1/(aalpha+b)+ 1/(abeta+b)=(abeta+b+aalpha+b)/((aalpha+b)(abeta+b))`

`implies1/(aalpha+b)+ 1/(abeta+b)=(a(beta+alpha)+2b)/((aalpha+b)(abeta+b))`

`implies1/(aalpha+b)+ 1/(abeta+b)=(a(alpha+beta)+2b)/(a^2alphabeta+ab(alpha+beta)+b^2)`

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