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Polynomials (1 Viewer)

FDownes

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More maths trouble, this time with polynomials;

A polynomial P(x) = (x - b)7 Q(x)

a) Show that P(b) = P'(b) = 0

This first part is pretty easy, but it's the second part I'm not sure about...

b) Hence find a and b if (x - 1)7 is a factor of x7 + 3x6 + ax5 + x4 + 3x3 + bx2 - x - 1

Who can help me out of this one?
 

tommykins

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a) is simple

b) Sub in x = 1 for P(x) and you get an equation with a and b.
Then sub x = 1 for P'(x) and you get another equation. => Simulateneous equations.

Note that (x-1)^7 is a factor therefore its multiplicty is 7.
 

FDownes

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Man, I should have seen that myself. For some reason I didn't make the connection between using the first part of the question in the solution to the second... :eek:
 

tommykins

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If q's come in parts, you wuold assume most of it is a "Hence".
 

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