I need help with D,F,H please. Exercise 2.38.(a) Demonstrate that a polynomial is completely determined by its coefficients. That is, if n andm are nonnegative integers and ao,..., an, bo, .. , bm are real numbers such that an, bm + 0andnconsta; · idg =Econsto; · idki=0i=0as relations, then n = m and a; = b; for all i = 0, ..., n. Hint: Induction on n starting at 0.33(b) If m1, m2, b1, b2 are real numbers, express lm,b2 o lm1,b1 as an affine function.(c) If m1, m2, b1, b2 are real numbers, express lm2.b2 + lm1.b1 as an affine function.(d) If m1, m2, b1, b2 are real numbers, express lIm2,62 · lmı,b1 as a quadratic function.(e) Demonstrate, if n and m are a1, ..., an and b1, ..., bm are real numbers, then) (Emn+mkconsta; · idgconsti, idg ) = £E consta;bk-iidi=0i=0k=0i=0by induction on n. This shows the degree of the product of two polynomials is the sum of theirdegrees.(f) Demonstrate by way of example. The degree of the sum of two polynomials can be equal tothe maximum of their degrees.(g) Demonstrate by way of example. The degree of the sum of two polynomials can be less thanthe maximum of their degrees.(h) Provide an example of two degree three polynomials whose sum has degree 0.

Name: I need help with D,F,H please. Exercise 2.38.(a) Demonstrate that a po
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: I need help with D,F,H please. Exercise 2.38.(a) Demonstrate that a polynomial is completely determined by its coefficients. That is, if n andm are nonnegative integers and ao,..., an, bo, .. , bm are real numbers such that an, bm + 0andnconsta; · id