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If x+a is a factor of polynomia X2+Px+g and x2+mx+n, prove that a=n-g/m-p

Posted by Neeti Gupta 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Since x + a is a factor of x²+ px + q
then (-a)²- 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- am + n = 0
{tex}\Rightarrow{/tex} a² - am + n= 0
{tex}\Rightarrow{/tex}a²= am - n........(ii)
From eq(i) and (ii), we get
am - n = ap - q
{tex}\Rightarrow{/tex}am - ap = n - q
Hence, a = {tex}\left[ \frac { n - q } { m - p } \right]{/tex}

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