11. Use the quadratic formula to explain why a quadratic polynomial function f(x) = ax? + bx +c is irreducible if, and only if, the discriminant b – 4ac is negative. Then use the discriminant to show that f(x) = 3x² + 2x + 6 is irreducible.

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Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method

A:

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A: A detailed solution is given below.

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A: We need to  Evaluate the quadratic form f(x) = xT Ax

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A: I am attaching image so that you understand each and every step.

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A: Solution of given question is written in below steps.