x^{2}+ax+b= 0  is an equation  \left ( where\; a,b\; \epsilon \; R \right )  , With one of roots as 2-3i, then a+b  equals

  • Option 1)

    6

  • Option 2)

    7

  • Option 3)

    8

  • Option 4)

    9

 

Answers (1)
H Himanshu

\because Coefficients are real, and one root is imaginary so other will be its conjugate pair i.e. 2+3i

\therefore Sum of roots = 4 = -a \Rightarrow a = -4

and product roots = 13 = b \Rightarrow b = 13

\therefore a+b = 9

\therefore Option (D)

 

Behaviour of Imaginary roots -

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

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Option 1)

6

This is incorrect

Option 2)

7

This is incorrect

Option 3)

8

This is incorrect

Option 4)

9

This is correct

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