In P₂, let (p(x), g(x)) = p(−1)q(−1) + p(0)q(0) +p(1)q(1). Let U = span{r², x + 1}. Find the polynomial in U that is closest to f(x) = 4x + 4. ]2²+ = 2+[

Q: consider the polynomial equation x3-7x2+14x-4=0 over the interval [0,2].

A: Iteration formula: The iteration formula of secant method is pn+1=pn-1-f(pn-1)pn-pn-1f(pn) -…

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

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Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: = x? – 5x + 7 has roots a and B. Use symmetric Suppose that f(x) functions to find a + B, aß, a² +…

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Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

A: Newton's divided differences interpolation

Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

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Q: Let F(a) be Z2. Show that a2 and a2+a are zeros of x3+x+1.

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

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Q: Consider the following Initial Value Problems (IVPs). dy dt dy ● dt dy dr dy dt + 2ty = te-t², y(0)…

A: Since you have asked multiple questions, we will solve the Question Q1 (a), (b) for you. If you want…

Q: Express the polynomial f(x) = 2x² + 3x³x²+x-2 in the form f(x)=b₁(x - 5)¹. i=0

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Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.

Q: List the zero's of f(x) = x³ + 3x² - 4x. X =

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

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Q: Vrite the polynomial P(x) = x-1 as a linear combination of P1(x) = 1-x+ 3x and Pa(x) =1-x+ 2x OA.…

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Q: Find a value for c so that the polynomial y^2+10y+c factors to (y+5)2.

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Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: Let f(x) = x3+5x+3. Construct the divided-difference table based on the nodes x0= 1, x1 = 2, x2 = 3,…

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Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

A: We use Newton's Divided Difference interpolation formula. x      x0      x1      x2      x3y      y0…