If the zeroes of p(x)=x2-p(x+1)-c are alpha and bita then (alpha +1)(b

1.	If the zeroes of p(x)=x2-p(x+1)-c are alpha and bita then (alpha +1)(bita+1)=
Answer» Given, {tex}\\alpha {/tex}\xa0and\xa0{tex}\\beta{/tex} are the zeroes of polynomial\xa0{tex}{x^2} - p(x + 1) + c{/tex}which can be written as\xa0{tex}{x^2} - px + c - p{/tex}So, sum of zeroes,\xa0{tex}\\alpha + \\beta = p{/tex}\xa0{tex}[\\because {/tex}\xa0sum of coefficients =\xa0{tex}\\frac{{ - (coefficient(x))}}{{\\operatorname{co} efficient({x^2})}}{/tex}]and product of zeroes\xa0{tex}\\alpha \\beta = c - p{/tex}\xa0{tex}[\\because {/tex}\xa0product of cofficients=\xa0{tex}\\frac{{constant\\_term}}{{coefficient({x^2})}}{/tex},]Also,\xa0{tex}(\\alpha + 1)(\\beta + 1) = 0{/tex}{tex}\\alpha\\beta + \\alpha + \\beta + 1 = 0{/tex}{tex} \\Rightarrow c - p + p + 1 = 0{/tex}{tex}\\Rightarrow c = - 1{/tex}

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