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2. Polynomials
easy
જો $a+b+c=0,$ હોય, તો $a^{3}+b^{3}+c^{3}=$..................છે.
A
$0$
B
$3abc$
C
$abc$
D
$2abc$
Solution
We know that
$a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)$
As $a+b+c=0,$ so, $a^{3}+b^{3}+c^{3}-3 a b c=(0)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)=0$
Hence, $a^{3}+b^{3}+c^{3}=3 a b c$
Therefore, $(b)$ $3 abc$ is the correct answer.
Standard 9
Mathematics
