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Question

If f(x)=4x33x2+2x+k and f(0)=1,f(1)=4, find f(x).

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Solution

It is given that f(0)=1 and f(1)=4 for the polynomial f(x)=4x33x2+2x+k, therefore, we substitute the values and find the value of k as shown below:

Whenf(0)=1f(0)=4(0)33(0)2+2(0)+k1=kWhenf(1)=4f(1)=4(1)33(1)2+2(1)+k4=43+2+k4=3+kk=43k=1

We conclude that, in both the cases k=1, thus, we substitute k=1 in f(x):

f(x)=4x33x2+2x+1

Hence, f(x)=4x33x2+2x+1.

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