Using the first four Hermite polynomials as a basis for P3, find the linear combination for the polynomial p(x)=7-12x8x² + 12x³

Q: I the zeros of the given quadratic polynomials, and verify the relationship between the oefficient…

A: Explanation and solutions is given below.....

Q: Generate the 2nd and 3rd degree Legendre polynomials.

A: Since we know the Rodrigue's formula of Legendre polynomial is Pn(x)=12nn!dndxnx2-1n For second…

Q: Find the quadratic polynomial if the zeroes of it are 2 and 1/3 respectively.

A: Find the quadratic polynomial

Q: F. Find the four roots of the polynomial z* + 16 and use these to factor z* + 16 into two quadratic…

A: We need to find the root of z4+16=0 Consider: z4+16=0⇒z4=-16⇒z22=-16⇒t2=-16…

Q: Find the degree of the polynomial using the method of finite differences. Then find the equation…

A: Please find attachment

Q: Forp(x)=a0+a1x+a2x2 andq(x)=b0+b1x+b2x2 fromP2,define ⟨p,q⟩=a0b0 +a1b1 +a2b2. Find the distance and…

A: Given for px=a0+a1x+a2x2 and qx=b0+b1x+b2x2 in ℙ2, define  p,q=a0b0+a1b1+a2b2

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

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Q: Find all zeros of P(x) = x* – 16 Factor the polynomial completely

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Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

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: (4) Find a polynomial that has 1+i and 1- i as zeros.

A: We have to find polynomial

Q: Find the quadratic polynomials whose zeroes (1)3,-4 (ii)2,1

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Q: Find a polynomial to interpolate the following data: (-1,1),(0,-1) and (1,1).

A: We have to use Lagrange's interpolation formula to find the polynomial from the given data.

Q: It is possible to write rk as a linear combination of Chebyshev's polynomials, for example Suppose…

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Q: Determine the 3rd degree polynomial which passes through the following points: 3 1 1 7 y 25

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Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…

Q: Let u (1,2.3.4) Vo ) (0.2.6,3 W: (1,1,1, Find t so that the angle between u-1lulliw and 2. v iv. 60

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