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9. If (x + a) is a factor of two polynomials x++px + q and x2 +mx + n then prove that an-am-p

Answer»

(x+a)=.: x=-a; x^2+px+q=(-a)^2+p(-a)+q=a^2-ap+q=0 ; x=-a^2; (-a)^2+m(-a)+n=a^2-ma+n; a^2-ap+q=a^2-ma+n; -ap+q=-ma+n; am-ap=n-q; a=n-q/m-p



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