JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Understanding +4 | -1

f\left( x \right)

is a polynomial of degree

n

with rational coefficients and

1 + 2i,\;2 - \sqrt 3

and 5 are three roots of

f\left( x \right) = 0

, then the least value of

n

View answer and explanation

Correct option: A

Option A (5) is correct because complex and irrational roots occur in conjugate pairs, so we must include

1-2i

and

2+\sqrt{3}

as roots, along with 5,

1+2i

and

2-\sqrt{3}

, giving a minimum degree of 5.

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