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[" EXAMPLE "17" Find a quadratic polynom...

[" EXAMPLE "17" Find a quadratic polynomial whose zeros are reciprocals of the zeros of the "],[" polynomial "f(x)=ax^(2)+bx+c,a!=0,c!=0" ."],[" SOLUTION Let "alpha" and "beta" be the zeros of the polynomial "f(x)=ax^(2)+bx+c." Then,"],[qquad alpha+beta=-(b)/(a)" and "alpha beta=(c)/(a)],[" Let "S" and "P" denote respectively the sum and product of the zeros of a polynomial whose "],[" Leros are "(1)/(alpha)" and "(1)/(beta)" .Then,"],[qquad S=(1)/(alpha)+(1)/(beta)=(alpha+beta)/(alpha)=-(b)/(c)" and "P=(1)/(alpha)times(1)/(beta)=(1)/(alpha beta)=(1)/(c)=(a)/(c)]

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