If alpha and beta are the zeros of the polynomial x2-5x+m such that al

1.	If alpha and beta are the zeros of the polynomial x2-5x+m such that alpha -beta = 1, find m
Answer» Since\xa0{tex}\\alpha , \\beta{/tex} are the zeros of the polynomial f(x) = x2\xa0- 5x + m.Compare f(x) = x2\xa0- 5x + m\xa0with ax2 + bx + c.So, a = 1 , b = -5 and c = m{tex}\\alpha + \\beta = - \\frac { ( - 5 ) } { 1 }{/tex}\xa0= 5{tex}\\alpha \\beta = \\frac { mk } { 1 } = m{/tex}Given,\xa0{tex}\\alpha - \\beta{/tex}\xa0= 1Now,\xa0{tex}( \\alpha + \\beta ) ^ { 2 } = ( \\alpha - \\beta ) ^ { 2 } + 4 \\alpha \\beta{/tex}{tex}\\Rightarrow{/tex}\xa0(5)2\xa0= (1)2\xa0+ 4m{tex}\\Rightarrow{/tex}\xa025 = 1 + 4m{tex}\\Rightarrow{/tex}\xa04m\xa0= 24{tex}\\Rightarrow{/tex}\xa0m\xa0= 6Hence the value of m\xa0is 6.

Discussion