Q4) Consider the Lagrange coefficient polynomial L2x(x) that are used for quadratic interpolation at the nodes xo,X1, and x2. Define g(x)=L2,0(x)+L21(x)+L22(x)-1. a. Show that g is a polynomial of degree < 2. b. Show that g(Xµ)=0 for k=0,1,2.

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Q: Show that if the quadratic polynomial f (x) = x2 + rx + s takes on both positive and negative…

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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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