If sum of the coefficients in the expansion 2×2−3cx+c2)17 is zero, then c is equal to

If sum of the coefficients in the expansion $(2 x^{2} - 3 c x + c^{2})^{17}$ is zero, then $c$ is equal to

A
2, 3
B
1, 2
C
1, 3
D
2, – 1

Solution:

Sum of the coefficients $= {(2 - 3 c + c^{2})}^{17}$

We are given ${(2 - 3 c + c^{2})}^{17} = 0$

$\Rightarrow c^{2} - 3 c + 2 = 0 \Rightarrow c = 1, 2$

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