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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Advance Math

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

Answer & Explanation Solved by verified expert

3.6 Ratings (497 Votes)

We havewhereandSince and are integers so and arealso integersNow putting in the expressionof weobtainThis shows that passes through thepoint The second statement is false The equationneed not have See Answer

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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 ?...

50.1K

Verified Solution

Question

Advance Math

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

Answer & Explanation Solved by verified expert

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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 ?...

50.1K

Verified Solution

Question

Advance Math

Suppose h, k, r, s, t?Z.Set a=3rt(2s+t) and b=3rs(s+2t).Provethe cubic polynomialf (x) = (x ? h)(x ? a ? h)(x ? b ? h) + kpasses through the point (h,k), has integer roots, has localextrema with integer coordinates, and has an inflectionpoint with integer coordinates.

Answer & Explanation Solved by verified expert

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