Show that if p(r) is a polynomial then h(x) (2-1)2")2(44)(x)122 -4)px) has a zero bet ween...
Show that if p(r) is a polynomial then h(x) (2-1)2")2(44)(x)122 -4)px) has a zero bet ween [-1,1 Show that if p(r) is a polynomial then h(x) (2-1)2")2(44)(x)122 -4)px) has a zero bet ween [-1,1
(i) Show that a non-zero polynomial in ??[?]Zp[x] has exactly ?−1p−1 associates. (ii) Let ?R be a field, 0≠?(?),?(?)∈?[?]0≠a(x),b(x)∈R[x]. Prove that ?(?)a(x) ?(?)b(x) are associates of each other if and only if ?(?)∣?(?)a(x)∣b(x)and ?(?)∣?(?)b(x)∣a(x). Q5 (4 points) (i) Show that a non-zero polynomial in Zp[x] has exactly p - 1 associates. a(x), b(x) E R[x]. Prove that a(x) b(x) are associates of each other if and only if a(x) | b(x) (ii) Let R be a field, 0 and b(x)...
2. Let Px(x) = 1, X = 1,2,3, 4, 5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P(3 < X < ), and P(1 < X < 2).
2. Show that a. P.(-x) =(-1)*P(x) b. Px.(0) - (-1) 2(!) c. P(0) - 0 3. Prove that j «P.com j«P«6?P.:(}é 4. Evaluate j <P:6)Ps(x)dt 5. Use Rodrigue's formula to calculate P (4)
The polynomial function (x) with real coefficients has 4 as a zero with multiplicity 2; 1 as a zero with multiplicity 1 and its degree is 3. Then 1 (x) can be written as
4. (a) Write the polynomial p(x) as a linear combination of the polynomials 1+r and r2 p(x) 3 3 Vrite the polynomial p(x) as a linear combination of the polynomials 1+
The polynomial of degree 4 The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = – 2. It goes through the point (5, 7). Find a formula for P(x). P(x) =
9. Show that for any non-zero real number a, the polynomial f(x)=" -a has no repeated roots in R. Hint: See 4.2.10 and 4.2.11 of the text.
(h) Define f : [0, 2] + R by 122 if 0 <<<1 f(x) = { ifl<152 Using the limit definition of the derivative and the sequence definition of the limit prove that f'(1) does not exist.
Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 4 - 2i and 2, with 2 a zero of multiplicity 2. R(x) = Show My Work (Optional) Submit Answer