In a quadratic equation with leading coefficient I, the negative of the coefficient of the linear term is the sum of the roots, and the constant term is the product of the roots (a) Prove these properties by expanding the factored quadratic (x Icirc raquo 1)(x Icirc raquo 2) 0 (b) Compare this result to equation (5) Explain how code termine from a matrix, without solving the character istic equation, the sum and product of its eigenvalues (c) Illustrate these results for the matrix 6 2

Question: In a quadratic equation with leading coefficient I, the negative of the coefficient of the linear term is the sum of the roots, and the

In a quadratic equation with leading coefficient I, the negative of the coefficient of the linear term is the sum of the roots, and the constant term is the product of the roots.
(a) Prove these properties by expanding the factored quadratic
(x - Î»1)(x - Î»2) = 0.
(b) Compare this result to equation (5). Explain how code-termine from a matrix, without solving the character-istic equation, the sum and product of its eigenvalues.
(c) Illustrate these results for the matrix

6 2

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