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If  \alpha ,\beta  are common roots between equations x^{3}+3x^{2}+2x+a= 0  and  x^{3}+5x^{2}+2x+b= 0  then  \alpha +\beta  equals

  • Option 1)

    -1

  • Option 2)

    0

  • Option 3)

    1

  • Option 4)

    2

 

Answers (1)

Common roots of given equations will also satisfy the equation obtained by substracting one from others. So \alpha ,\beta are also roots of 2x^{2}+\left ( b-a \right )=0\: \Rightarrow \: \alpha +\beta =0

\therefore Option (B)

 

Nature of Common roots -

If  P_{1}\left ( x \right )= 0  and  P_{2}\left ( x \right )= 0 are two polynomial equations with same common root then any third polynomial equation obtained with algebra of first two will also have those common roots.

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Option 1)

-1

This is Incorrect.

Option 2)

0

This is correct.

Option 3)

1

This is Incorrect.

Option 4)

2

This is Incorrect.

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