If p and q are the roots of equation x^2+px-q=0 then find the value of

1.	If p and q are the roots of equation x^2+px-q=0 then find the value of p and q.
Answer» {tex}x^2\xa0+\xa0px -\xa0q = 0{/tex}and roots are given as p and qsum of the roots\xa0= {tex}\\frac{ - coefficient \\: of \\: x}{coefficient \\: of \\: {x}^{2} }{/tex}So,{tex}\\Rightarrow{/tex}\xa0{tex}p + q ={/tex}\xa0{tex}\\frac{-p}{1}{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}p + q = -p{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}q = -p -p{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}q = -2p{/tex} ..(1)Now, product\xa0of roots\xa0= {tex}\\frac{constant \\: term \\: }{coefficient\\ of\\: {x}^{2} } {/tex}So,pq = {tex}\\frac{-q}{1}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0pq = -q\xa0{tex}\\Rightarrow{/tex}\xa0p =\xa0{tex}\\frac{-q}{q}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0p = -1 ..(2)Put the value of (2) in (1), we get{tex}\\Rightarrow{/tex}\xa0{tex}q = -2(-1) = 2{/tex}.

Discussion