If ${\rm{g}}\;\left( x \right)$ and $h\left( x \right)$ are two polynomials such that the polynomial $P\left( x \right) = {\rm{g}}\left( {{x^3}} \right) + x\;h\left( {{x^3}} \right)$ is divisible by ${x^2} + x + 1,$ then which one of the following is not true?

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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\mathrm{g}\;\left( x \right)

and

h\left( x \right)

are two polynomials such that the polynomial

P\left( x \right) = \mathrm{g}\left( {{x^3}} \right) + x\;h\left( {{x^3}} \right)

is divisible by

{x^2} + x + 1,

then which one of the following is not true?

View answer and explanation

Correct option: B

\mathrm{g}\left( 1 \right) = h\left( 1 \right) \ne 0

Option B (

\mathrm{g}\left( 1 \right) = h\left( 1 \right) \ne 0

) is not true because the correct deduction is that

\mathrm{g}\left( 1 \right) = h\left( 1 \right) = 0