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Relation between Roots and Coefficients for Quadratic

If x3-2x2 -...

Question

If $x^{3} - 2 x^{2} - x + 2 = (x - a) (x + b) (x - c)$ .Find $a + b + c$

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Solution

$x^{3} - 2 x^{2} - x + 2 = x^{2} (x - 2) - 1 (x - 2) = (x^{2} - 1) (x - 2) = (x - 1) (x + 1) (x - 2) c o m p a r e i t w i t h (x - a) (x + b) (x - c), w e g e t a = 1, b = 1 a n d c = 2 H e n c e a + b + c = 4$

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