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प्रश्न
If α, β are the zeros of polynomial f(x) = x2 − p (x + 1) − c, then (α + 1) (β + 1) =
विकल्प
c − 1
1 − c
c
1 + c
उत्तर
Since `alpha` and `beta` are the zeros of quadratic polynomial
f(x) = x2 − p (x + 1) − c
`= x^2 - px p -c`
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`=-((-p)/1)`
`= p`
`alpha xx ß = (\text{constat term})/(text{coefficient of} x^2)`
`= (-p-c)/1`
`= -p-c`
We have
`(alpha+1)(beta+1)`
`= alpha beta+ beta + alpha +1`
`= alphabeta + (alpha+beta)+1`
`= - p-c +(p)+1`
`- cancel(p)- c+ cancel(p) +1`
`= -c+1`
`= 1-c`
The value of `(alpha +1) (beta +1)` is ` 1- c`.
Hence, the correct choice is `(b)`
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