AP EAMCET202125 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

If x^2+p x+1 is a factor of a x^3+b x+c , then

Options

Aa^2+c^2=-a b
Ba^2-c^2=-a b
Ca^2-c^2=a b
Da^2+c^2=a b

Correct answer

C. a^2-c^2=a b

Step-by-step solution

We have, x^2+p x+1 is a factor of a x^3+b x+c=0 a x^3+b x+c= (x^2+p x+1 )(a x+ ) a x^3+b x+c=a x^3+(p a+ ) x^2+(p +a) x+ Equating the coefficient of x^3, x^2, x and constant term, we get aligned p a+ & =0, & p +a=b, & =c p & = -c a & & [ =c] aligned Putting the values of p and in p +a=b aligned (- c a )(c)+a & =b -c^2+a^2 & =a b a^2-c^2=a b aligned

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