If a and B are the zeroes of the polynomial F(X)=x^2-6x+k,find the value of k,such that a^2+b^2=40

If a and B are the zeroes of the polynomial F(X)=x^2-6x+k,find the val

1.	If a and B are the zeroes of the polynomial F(X)=x^2-6x+k,find the value of k,such that a^2+b^2=40
Answer» {tex}\\alpha + \\beta = - \\frac { b } { a }{/tex}{tex}= \\frac { - ( - 6 ) } { 1 }{/tex}\xa0= 6and\xa0{tex}\\alpha \\beta = \\frac { c } { a } = \\frac { k } { 1 } = k{/tex}{tex}\\therefore{/tex}{tex}{/tex}\xa0{tex}\\alpha ^ { 2 } + \\beta ^ { 2 } = ( \\alpha + \\beta ) ^ { 2 } - 2 \\alpha \\beta = 40{/tex}{tex}\\Rightarrow\\ {/tex}\xa0(6)2\xa0- 2k = 40{tex}\\Rightarrow\\ {/tex}\xa036 - 2k = 40{tex}\\Rightarrow {/tex}\xa0-2k = 4{tex}\\Rightarrow{/tex}\xa0k = -2