If $1,2,3$ and 4 are the roots of the equation $x^4+a x^3+b x^2+c x+d=0$, then $a+2 b+c$ is equal to

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Aicharya · Accepted Answer

If $1,2,3,4$ are the roots of the equation $\begin{gathered}x^4+a x^3+b x^2+c x+d=0, 	ext { then } \ (x-1)(x-2)(x-3)(x-4) \ =x^4+a x^3+b x^2+c x+d \ \Rightarrow \quad\left(x^2-3 x+2ight)\left(x^2-7 x+12ight) \ =x^4+a x^3+b x^2+c x+d \ \Rightarrow \quad x^4-10 x^3+35 x^2-50 x+24 \ \quad=x^4+a x^3+b x^2+c x+d \ \Rightarrow \quad a=-10, b=35, c=-50, d=24\end{gathered}$ Now, $a+2 b+c=-10+2 	imes 35-50$ $=10$

If $1,2,3$ and 4 are the roots of the equation $x^4+a x^3+b x^2+c x+d=0$, then $a+2 b+c$ is equal to

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