If the difference between the roots of the equation x2+px+8=0, then wh

1.	If the difference between the roots of the equation x2+px+8=0, then what is the value of p?
Answer» Ans, Let\xa0{tex}\\alpha \\ and \\ \\beta {/tex}\xa0be the roots of equation.Then\xa0{tex}\\alpha \\ - \\beta = 2 \\ \\ ........... (1) [Given ]{/tex}We know,\xa0Sum of roots =\xa0{tex}-{b\\over a}{/tex}{tex}\\alpha \\ + \\beta = -p \\ .............. (2) {/tex}Adding (1) and (2), we get{tex}2\\alpha = 2- p {/tex}=>\xa0{tex}\\alpha = {2-p\\over 2}{/tex}Subtracting (1) from (2), we get\xa0{tex}2\\beta = - p -2 {/tex}=>\xa0{tex}\\beta = {-p-2\\over 2}{/tex}Also,Product of roots =\xa0{tex}c\\over a{/tex}=>\xa0{tex}\\alpha \\times \\beta = 8{/tex}=>\xa0{tex}{2-p\\over 2} \\times {-2-p\\over 2} = 8 {/tex}=>\xa0{tex} -4 -2p+2p+p^2 = 32{/tex}=> p2\xa0= 36=> p = -6, 6\xa0

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