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  • Confused! kindly explain, - Complex numbers and quadratic equations - JEE Main-6

If x^{3}+5x^{2}+px+q= 0  and x^{3}+7x^{2}+px+r= 0  have two common roots. Then the sum of their third roots is 

  • Option 1)

    -10

  • Option 2)

    -12

  • Option 3)

    -14

  • Option 4)

    -16

 

Answers (1)

best_answer

Common roots will also satisfy the difference of two equations.

\therefore Common roots are also roots of 2x^{2}+\left ( r-q \right )=0

\Rightarrow Sum of common roots = 0

x^{3}+5x^{2}+px+q=0 has sum of roots = -5

Where sum of two roots which are in common is zero so third root is -5

Similarly, third root of 2^{nd} equation is -7

\therefore Sum of 3^{rd} roots = -12

\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.

-

 

 


Option 1)

-10

This is incorrect

Option 2)

-12

This is correct

Option 3)

-14

This is incorrect

Option 4)

-16

This is incorrect

Posted by

Himanshu

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