Find the unique quadratic polynomial y = ax² +bx+c that passes through the three points (1, 1), (3,5), and (-2,0) in the x-y plane. (Hint: this will involve a linear system where a, b, and c are the unknowns.) How many data points (x, y) should be needed to uniquely determine the coef- ficients of an nth degree polynomial anx"+an-1xn-1+...+ a₁x+ao? Explain your answer in terms of linear systems.

Q: 13. Find the equation of the third degree polynomial containing the points (1, -7), (0, 4),(3, -2)…

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Q: e down a polynomial of degree exactly 4 that interpolates the four points: (-1,-5 1), (2, 1), (3,…

A: We have to find the polynomial equation from given points.

Q: 2. Find the polynomial the passes through the following points (0,0), (2, —2), (4,0)

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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: OF dy F, dr OF F, For F(x, y) = 0, 1. Use partial derivatives (i.e. the formulas above) to find at x…

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Q: Find all real solutions of the polynomial equation x* - 7x + 42x - 36 = 0. х%3D 1,-36, 12 х%3D 1,-7,…

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

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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: A polynomial which goes through the point (1,4) and has zeros at x=0,x=3 and x=-2

A: Given:A polynomial pass through the point (1,4) and has zeroes at x=0, x=3 and x=-2.

Q: determine the polynomial function whose graph passes through the given points (2, 4), (3, 6), (5,…

A: We are given the points (2, 4), (3, 6), (5, 10). (2, 4): 4 = 2*2 (3, 6): 6 = 2*3 (5, 10): 10 = 2*5…

Q: Find the quadratic polynomial whose graph goes through the points (-1, 3), (0, 1), and (1,7). f(x) =

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Q: Suppose experimental data are represented by a set of points in the plane. An interpolating…

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