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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2023 · Mathematics · Quadratic Equation

If 2-i 3 where i= -1 is a root of the equation x^2+a x+b=0 , then...

If 2−i32-i \sqrt{3} where i=−1i=\sqrt{-1} is a root of the equation x2+ax+b=0x^2+a x+b=0, then what is the value of (a+b)(a+b) ?

Options

  1. A−11-11
  2. B−3-3
  3. C00
  4. D33

Correct answer

D. 33

Step-by-step solution

If 2−3i2-\sqrt{3} i is one root. ⇒2+3i\Rightarrow \quad 2+\sqrt{3} i is other root ∴−aC=\therefore \quad-a \mathrm{C}= Sum of roots ⇒−a=2−3i+2+3i=4⇒a=−4\Rightarrow-\mathrm{a}=2-\sqrt{3} i+2+\sqrt{3} i=4 \Rightarrow a=-4 and b=b= product of roots b=(2−3i)(2+3i)=4+3=7a+b=−4+7=3b=(2-\sqrt{3} i)(2+\sqrt{3} i)=4+3=7a+b=-4+7=3
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