If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) |1 f(b) (x-b) f(c) (x-c) 1 a 1 b 1 c a a² b 6² 222 C f(x) (x-a)(x-b)(x-c)

Q: Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For…

A: We will use repeated differentiation to prove this

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Firstly make the divided difference table x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl Pxi ,…

Q: If f (x) = 2 – x² +x° and ƒ(a) = 2, then all possible values of a are (A) 0 and 1 only (B) 0,1, and…

A: f(x)=2-x2+x3 f(a)=2 put x=2 f(2)=  2-22+23 =2-4+8 =6

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

A: The objective is to find the value of 2c3-c2

Q: Given a polynomial f(x), if (x − 2) is a factor, what else must be true?  a) f(0) = 2 f b) (0) =…

A: NOTE: Refresh your page if you can't see any equations. . use the remainder theorem to solve this…

Q: a) f(x) is a polynomial function. If f'(x) has a degree of 7, what is the degree of f(x)? b) Write a…

A:

Q: A basic fact of algebra states that c is a root of a polynomial f if and only if f(x) = (x -…

A: (a) x 5 + 2x 4 - 4x 3 - 8x2 - x + 2  To find whether c=-1 is a multiple root we have to subs. c=-1…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Newton's Divided Difference table is given by x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl…

Q: If fis a polynomial and f (z) = i, thenf(2) = i True B) False

A:

Q: Graph the polynomial function f(x)--(x + 1)(x - 1) (x - 3)²

A: Given: polynomial function f(x)=-(x+1)(x-1)2(x-3)2. To be find: graph the polynomial function.…

Q: If f(x) is a polynomial function satisfying f(x) ·ƒ ( ² ) = f(x) + f ( ² ) a and f(4) = 65, then…

A:

Q: Show that f (x) = x2 + 3x−1 and g(x) = 3x3 − 9x + x−2 are rational functions—that is, quotients of…

A: To show: That the functions are rational function: Given: The functions are fx=x2+3x-1 and…

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

A:

Q: Prove that you can find a polynomial p(x) = Ax2 + Bx + C that passes through any three points (x1,…

A: we have to prove that we can always find a polynomial p(x) = Ax2 + Bx + C that  passes through any…

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: For the polynomials p(x)=4x* – 3x² +x -1 and d(x) =x² – 1, write in the form p(x)= d(x)q(x)+r(x).

A:

Q: Create a polynomial function of the form: f(x) = a (bx + e)(cx +g}*(dx + h)°, with the following…

A:

Q: 5. Obtain a polynomial P(x) such that f(x) = P₁(x) given the table -1 -3 x₁ f(x₂) -2 -13 1 -1 2 -9 3…

A:

Q: What are the zeros of the polynomial function f(x) = -x³ + 2x? + x – 2? O (0,0), (1,0), 2,0) O…

A:

Q: | Let f(x) = 2x³+3x²-x-5. Determine f[x0, x₁, x2, x3] and ƒ [x0, X₁, X2, X3, X4].

A:

Q: The polynomial f(x) = x2021 + x2020 +9.03x + 1 has at least one real root.

A: Explanation of the answer is as follows