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The equation of smallest degree with real coefficients having 2 + 3i as one of the roots is
  • a)
    x2 − 4x + 13 = 0
  • b)
    x2 + 5x + 6 = 0
  • c)
    x2 − 2x + 1 = 0
  • d)
    x2 + 2x + 1 = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The equation of smallest degree with real coefficients having 2 + 3i a...
Since 2+ 3i is a root
∴ 2-3i is also a root
Hence, required equation is
x2-(sum of roots) x + (product of roots) = 0
Sum of roots=2+3i+2-3i=4
Product of roots
=(2+31) (2-3)=4-9i2-13 [∵ i= -1]
So, equation is x- 4x + 13 = 0.
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Community Answer
The equation of smallest degree with real coefficients having 2 + 3i a...
The equation with smallest degree having 2 + 3i as one of the roots can be found using the conjugate root theorem.

Since 2 + 3i is a root, its conjugate 2 - 3i must also be a root.

Therefore, the equation with smallest degree having 2 + 3i as one of the roots is:

(x - (2 + 3i))(x - (2 - 3i))
= (x - 2 - 3i)(x - 2 + 3i)
= (x - 2)² - (3i)²
= (x - 2)² - 9i²
= (x - 2)² - 9(-1)
= (x - 2)² + 9

So, the equation is x² - 4x + 4 + 9 = x² - 4x + 13.

The equation of smallest degree with real coefficients having 2 + 3i as one of the roots is x² - 4x + 13.
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The equation of smallest degree with real coefficients having 2 + 3i as one of the roots isa)x2 − 4x + 13 = 0b)x2 + 5x + 6 = 0c)x2 − 2x + 1 = 0d)x2 + 2x + 1 = 0Correct answer is option 'A'. Can you explain this answer?
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The equation of smallest degree with real coefficients having 2 + 3i as one of the roots isa)x2 − 4x + 13 = 0b)x2 + 5x + 6 = 0c)x2 − 2x + 1 = 0d)x2 + 2x + 1 = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of smallest degree with real coefficients having 2 + 3i as one of the roots isa)x2 − 4x + 13 = 0b)x2 + 5x + 6 = 0c)x2 − 2x + 1 = 0d)x2 + 2x + 1 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of smallest degree with real coefficients having 2 + 3i as one of the roots isa)x2 − 4x + 13 = 0b)x2 + 5x + 6 = 0c)x2 − 2x + 1 = 0d)x2 + 2x + 1 = 0Correct answer is option 'A'. Can you explain this answer?.
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