Question

Find rational roots of the polynomial f (x) = 2x3 + x2 - 7x-6.​

Answer 1

2x³ + x² - 7x -6 = 0

2x³ + 2x² - x² - x - 6x - 6 = 0

2x²(x + 1) -x(x + 1) -6(x + 1) = 0

(x + 1)(2x² - x - 6) = 0

(x + 1) ( 2x² - 4x + 3x - 6) = 0

(x + 1) (2x(x -2) + 3(x - 2)) = 0

(x + 1)(2x + 3)(x - 2) = 0

x = -1, x = -3/2, x = 2

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Answer 2

$Solve for x:x^3-7 x+6 = 0The left hand side factors into a product with three terms:(x-2) (x-1) (x+3) = 0Split into three equations:x-2 = 0 or x-1 = 0 or x+3 = 0Add 2 to both sides:x = 2 or x-1 = 0 or x+3 = 0Add 1 to both sides:x = 2 or x = 1 or x+3 = 0Subtract 3 from both sides:Answer: | x = 2 or x = 1 or x = -3$