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  • Help me understand! - Complex numbers and quadratic equations - JEE Main-2

If x^{2}+2x+5= 0 and x^{2}+ax+b= 0  have a common root \left ( Where\; a,b\; \epsilon \; N \right ) then b-a equals

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

best_answer

x^{2}+2x+5=0 have imaginary roots and it has to have common root with x^{2}+ax+b=0 Where, a,b\: \epsilon \: N , which is real number.

so one root can't be common, both roots will be common . So 

\frac{1}{1}=\frac{2}{a}=\frac{5}{b}\: \Rightarrow \, a=2\, and\, b=5

\therefore b-a=3

\therefore  Option (C)

 

Behaviour of Imaginary roots -

For any polynomial equation with real coefficients, Imaginary roots always occur in conjugate pair.

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Option 1)

1

This is incorrect

Option 2)

2

This is incorrect

Option 3)

3

This is correct

Option 4)

4

This is incorrect

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