if x=1 is a zero of the polynomial f(x)=x2-2x2+4x+k
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In the given polynomial f(x)=x
3
−2x
2
+4x+k, substitute x=1 as shown below:
f(1)=1
3
−(2×1
2
)+(4×1)+k=1−2+4+k=3+k
Therefore, f(1)=3+k.
Since it is given that x=1 is a zero of the polynomial f(x)=x
3
−2x
2
+4x+k, therefore f(1)=0 that is:
3+k=0
⇒k=−3
Hence k=−3.
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