Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial f (x) = (x...

Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial

f (x) = (x − h)(x − a − h)(x − b − h) + k
passes through the point (h,k), has integer roots, has local extrema with integer coordinates, and has an inflection

point with integer coordinates.

Expert Solution

Colby Messinger answered 2 years ago

Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial f (x) = (x...

Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial f (x) = (x − h)(x − a − h)(x − b − h) + k passes through the point (h,k), has integer roots, has local extrema with integer coordinates, and has an inflection point with integer coordinates.

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Use induction to prove Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x)∈Pn(R) there exist scalars c0, c1, ...., cn such that g(x)=c0f(x)+c1f′(x)+c2f′′(x)+⋯+cnf(n)(x), where f(n)(x)denotes the nth derivative of f(x).

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Let f(t)=5t2−t. a) Find f(t+h): b) Find f(t+h)−f(t): c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on...

Let f(t)=5t2−t. a) Find f(t+h): b) Find f(t+h)−f(t): c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on top of fraction and h is on bottom) d) Find f′(t): pls circle the 4 answers

Let L = {x = a r b s c t | r + s =...

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Question

Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial f (x) = (x...

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Expert Solution

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Suppose h, k, r, s, t∈Z.Set a=3rt(2s+t) and b=3rs(s+2t).Prove the cubic polynomial f (x) = (x...

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