If (x+a)is a factor of the polynomialxsquare+px+q and x square +mx+n then prove that a=n-q/m-p

If (x+a)is a factor of the polynomialxsquare+px+q and x square +mx+n t

1.	If (x+a)is a factor of the polynomialxsquare+px+q and x square +mx+n then prove that a=n-q/m-p
Answer» Since x + a is a factor of x2+ px + qthen (-a)2\xa0- pa + q = 0{tex}\\Rightarrow{/tex}a2 = pa -q ..........(i)also (x + a) is a factor of x2+ mx + n then we get(-a )2\xa0- am + n = 0{tex}\\Rightarrow{/tex} a2 - am + n= 0{tex}\\Rightarrow{/tex}a2\xa0=\xa0am - n........(ii)From eq(i) and (ii), we getam - n = ap - q{tex}\\Rightarrow{/tex}am - ap = n - qHence, a =\xa0{tex}\\left[ \\frac { n - q } { m - p } \\right]{/tex}