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JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    Let a, b, c be non-zero real numbers, If the system of equations
    \[y+z=a+2x\]
    \[x+z=b+2y\]
    \[x+y=c+2z\]
    is consistent and \[b=4a+\frac{c}{4}\], then the absolute value of sum of roots of the equation \[a{{x}^{2}}+bx+c=0\], is equal to

    A)  1                                            

    B)  2

    C)  3                                            

    D)  4

    Correct Answer: C

    Solution :

    \[\left. \begin{matrix}    y+z=a+2x  \\    x+z=b+2y  \\    x+y=c+2z  \\ \end{matrix} \right\}\] adding \[a+b+c=0\]             Given 16a - 4b + c = 0 \[\therefore \,\,x=-4\] \[a{{x}^{2}}+bx+c\left\langle \begin{align}   & 1 \\  & -4 \\ \end{align} \right.\] Sum of roots = - 3 \[\Rightarrow \] absolute value of sum of roots \[=\,|-3|=3\]


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