Question

Find a second-degree polynomial P such that P(4)=5, P'(4)=3, and P"(4)=3

Polynomials
ANSWERED
asked 2021-02-02

Find a second-degree polynomial P such that \(P(4)=5\), \(P'(4)=3\), and \(P"(4)=3\)

Answers (1)

2021-02-03

Consider second degree polynomial \(P(x)=a+bx+cx^{2}\) such that
\(P(4)=5, P′(4)=3\), and \(P′′ (4)=3.\)
\(P(4)=5P(4)=5\) gives us
\(a+4b+16c=5\).
Now differentiating P, we get \(P′=b+2cx\). Now putting \(x=4\), we get
\(b+8c=3\).
Now differentiating P′, we get \(P''=2cP\). Now putting \(x=4,\) we get
\(b+12=3\Rightarrow b=−9.\)
Now putting \(c=\frac{3}{2}\) and \(b= -9\ in\ {eq1}\) we get

\(a−36+48=5\Rightarrow a=−7.\)

So required second degree polynomial is \(P(x)=−7−9x+(\frac{3}{2})x2\)

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