The quadratic equation x^{2}+bx+c=0 with real coefficients b and c, has a complex root\sqrt 3 - i , then which of the following represents the value of c-ib ?

  • Option 1)

    4-2\sqrt3 i

  • Option 2)

    4+2\sqrt3 i

  • Option 3)

    2\sqrt3 +4i

  • Option 4)

    2\sqrt3 -4i

 

Answers (1)
V Vakul

As learnt in

To form a Quadratic Equation given the roots -

x^{2}-Sx+P= 0

- wherein

S = Sum of roots

P = Product of roots

 

 x^{2}+bx+c=0

\Alpha\alpha = \sqrt 3 -i    ;    \beta = \sqrt 3 +i

-b=2 \sqrt 3\:\:\:\:\:\: \Rightarrow b=-2 \sqrt 3

c= \alpha \beta = (\sqrt3-i) (\sqrt3+i)=4

c-ib=4+2\sqrt 3 i


Option 1)

4-2\sqrt3 i

This option is incorrect.

Option 2)

4+2\sqrt3 i

This option is correct.

Option 3)

2\sqrt3 +4i

This option is incorrect.

Option 4)

2\sqrt3 -4i

This option is incorrect.

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