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  • Help me please, - Complex numbers and quadratic equations - JEE Main-6

2x^{3}+mx^{2}-13x+n=0 has roots 2 and 3 then m+n equals 

  • Option 1)

    10

  • Option 2)

    15

  • Option 3)

    20

  • Option 4)

    25

 

Answers (2)

best_answer

Three roots are  2,3,x\Rightarrow 2(3)+3(x)+x(2)=\frac{-13}{2}\Rightarrow x=\frac{-5}{2}

\\*\therefore roots\; \; are\; \; 2,3,\frac{-5}{2}\Rightarrow Sum=\frac{-m}{2}=\frac{5}{2}\Rightarrow m=-5\\*and\; \; 2(3)\left ( \frac{-5}{2} \right )=product=\frac{-n}{2}\Rightarrow n=30\\*\therefore m+n=25

 

 

Sum of product of pair of roots in cubic equation -

\alpha \beta +\beta \gamma +\gamma \alpha = \frac{c}{a}

- wherein

ax^{3}+bx^{2}+cx+d= 0

is the cubic equation

 

 


Option 1)

10

This is incorrect

Option 2)

15

This is incorrect

Option 3)

20

This is incorrect

Option 4)

25

This is correct

Posted by

prateek

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25

Posted by

Rekha

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