(a) 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.) (b) How many data points (x, y) should be needed to uniquely determine the coefficients of an nth degree polynomial anx" +an-1x²−¹+...+a₁x+ªo? Explain your answer in terms of linear systems.

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A: We will find out the required solution.

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A: We have to solve

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A: To find particular solution we use the method of variation of parameters

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A: Given : Differential Equation x2-x+1y''-y'-y=0To find : atleast six non-zero terms of the power…

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A: An example of the first order linear differential equation is given below.

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Q: AD0²S

A: The solutions of the given partial differential Equation is in below

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