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Question
If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =
Options
1
0
-1
2
Solution
Since `alpha` and `beta` are the zeros of quadratic polynomial
f(x) = x2 − p(x + 1) − c
`f(x)= x^2 - px -p-c`
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`= -(-p/1)`
`= p`
`alphabeta= (\text{Coefficient of x})/(\text{Coefficient of}x^2)`
`= (-p-c)/1`
`= -p-c`
We have
`0 = (alpha + 1)(beta+1)`
`0=alpha beta + (alpha +beta)+1`
`0 = - cancel(p)-c + cancel(p) +1`
`0 = -c +1`
The value of c is 1.
Hence, the correct alternative is `(a)`
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