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  • Can someone explain - Complex numbers and quadratic equations - JEE Main-5

If 2+\sqrt{3} is a root of x^{2}+ax+b= 0  \left ( Where\; a,b\: \epsilon\: Q \right ) then a+b  equals

  • Option 1)

    0

  • Option 2)

    -1

  • Option 3)

    -2

  • Option 4)

    -3

 

Answers (1)

\because \: a,b\, \epsilon \, Q and one root is 2+\sqrt{3}, So other root is 

2+\sqrt{3}\: \Rightarrow \: Sum\, =-a=4\: and\: product\, =b=1

\therefore \: a=-4\: and\: b=1\: \Rightarrow a+b=-3

\therefore Option (D)

 

Nature of roots (Irrational) -

a,b,c\in Q ( Rational no.)

If P+\sqrt{q}\left ( P,q \in Q \right ) is an irrational root

\Rightarrow P-\sqrt{q} is also a root

- wherein

ax^{2}+bx+c=0

is a quadratic equation

 

 


Option 1)

0

This is incorrect

Option 2)

-1

This is incorrect

Option 3)

-2

This is incorrect

Option 4)

-3

This is correct

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subam

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