Find constants b and c in the polynomial p (x )equals x squared plus bx plus cp(x)=x2+bx+c such that ModifyingBelow lim With x right arrow 4 StartFraction p (x )Over x minus 4 EndFraction equals 10limx→4 p(x) x−4=10. Are the constants unique?

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carloggrlj carloggrlj · Answer 1 · 2020-01-24T13:02:17+01:00

Answer:

b=2

c=-24.01

Step-by-step explanation:

If I understood your question right you need to find the constants b and c in the polynomial:

[tex]p(x)=x^2+bx+c[/tex]

such that:

[tex]\lim_{x\to4} \frac{x^2+bx+c}{x-4}[/tex]

In order to get a system of two equations you can find limes when x goes to 4 from the right side or from the left side.

I solved this using a number that is close to 4. When it goes from right I used 4.1 and from left 3.9. This way you get two equations:

[tex]16.81+4.1b+c=1\\15.21+3.9b+c=-1[/tex]

When you solve the system you get the answers above.