Determine coefficients a and b such that p(x)=x2 ax b satisfies p(1)=5 and p′(1)=11.

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23-02-2017
Mathematics

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Determine coefficients a and b such that p(x)=x2 ax b satisfies p(1)=5 and p′(1)=11.

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LammettHash LammettHash · Answer 1 · 2017-02-23T22:43:48+01:00

LammettHash LammettHash

23-02-2017

[tex]p(x)=x^2+ax+b[/tex]
[tex]p'(x)=2x+a[/tex]

Given that [tex]p'(1)=11[/tex], you have

[tex]p'(1)=2+a=11\implies a=9[/tex]

and given that [tex]p(1)=5[/tex], you have

[tex]p(1)=1+9+b=5\implies b=-5[/tex]

So you get

[tex]p(x)=x^2+9x-5[/tex]

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