If alpha and beta are zeroes of the polynomial f(x)=x^2-x-k such that alpha - beta =9. Find k?

If alpha and beta are zeroes of the polynomial f(x)=x^2-x-k such that

1.	If alpha and beta are zeroes of the polynomial f(x)=x^2-x-k such that alpha - beta =9. Find k?
Answer» Since\xa0{tex}\\alpha \\text { and } \\beta{/tex}\xa0are the zeroes of the polynomial, then{tex}{/tex}{tex}\\alpha + \\beta = - \\frac { \\text { Coefficient of } x } { \\text { Coefficient of } x ^ { 2 } }{/tex}{tex}{/tex}{tex}{/tex}{tex}\\Rightarrow\\ \\alpha + \\beta = - \\left( \\frac { - 1 } { 1 } \\right) = 1{/tex}.........(i)Given,\xa0{tex}\\alpha - \\beta = 9{/tex}...............(ii)Solving (i) and (ii),\xa0{tex}\\alpha = 5 , \\beta = - 4{/tex}{tex}\\alpha \\beta = \\frac { \\text { Constant term } } { \\text { Coefficient of } x ^ { 2 } }{/tex}{tex}\\Rightarrow\\ \\alpha \\beta = - k{/tex}{tex}\\Rightarrow\\ {/tex}(5)(-4) = -k{tex}\\Rightarrow{/tex}k = 20So,required value of k is 20