If x = 1 is a zero of the polynomial f (x) = x^{3} – 2x^{2} + 4x + k, write the value of k.

Given,

f(x) = x^{3} – 2x^{2} + 4x + k

x = 1 is a zero,

So,

Keeping x = 1 we get,

f(1) = 1^{3} – 2(1)^{2} + 4×1 + k

f(1) = 1 – 2 + 4 + k

f(1) = 5 – 2 + k

f(1) = 3 + k

– 3 = k

So we get,

k = – 3

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