$x^{2}+ax+b= 0$  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

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.

-

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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