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Confused! kindly explain, - Complex numbers and quadratic equations - JEE Main-9

If \alpha ,\beta are roots of x^{2}+x+2= 0, then the equation whose roots are \alpha ^{2}+1\beta ^{2}+1 is

  • Option 1)

    x^{2}-x-2= 0

  • Option 2)

    x^{2}-x+2= 0

  • Option 3)

    x^{2}+x-2= 0

  • Option 4)

    x^{2}+x+2= 0

 
Answers (1)
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S subam

\\*S=(\alpha ^{2}+1)+(\beta ^{2}+1)=(\alpha +\beta )^{2}-2\alpha \beta +2\\*S=1-2(2)+2=-1\Rightarrow S=-1\\*P=(\alpha ^{2}+1)(\beta ^{2}+1)=(\alpha \beta )^{2}+(\alpha ^{2}+\beta ^{2})+1\\*P=(\alpha \beta )^{2}+(\alpha +\beta )^{2}-2\alpha \beta +1\\*P=4+1-2(2)+1=2\Rightarrow P=2\\*\therefore Equation\; :\, \; x^{2}+x+2=0

 

To form a Quadratic Equation given the roots -

x^{2}-Sx+P= 0

- wherein

S = Sum of roots

P = Product of roots

 

 


Option 1)

x^{2}-x-2= 0

This is incorrect

Option 2)

x^{2}-x+2= 0

This is incorrect

Option 3)

x^{2}+x-2= 0

This is incorrect

Option 4)

x^{2}+x+2= 0

This is correct

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