Question

Find the rational roots of the following polynomials:- f(x)=2x^3+x^2-7x-6

Answer 1

Answer:

{- 1.5, - 1, 2}

Step-by-step explanation:

Factor of (- 6) are - 1, - 2, - 3, - 6, 1, 2, 3, 6

f(-1) = 2(- 1)³ + (- 1)² - 7(- 1) - 6 = 0 ⇒ (x + 1) is factor of given polynomial

(2x³ + x² - 7x - 6) ÷ (x + 1) = 2x² - x - 6

2x² - x - 6 = 0

D = b² - 4ac = (- 1)² - 4×2×(- 6) = 49

$x_{12}$ = (- b ± √D) / 2a = [- (- 1) ± √49] / 2×2

$x_{1}$ = (1 + 7) ÷ 4 = 2

$x_{2}$ = (1 - 7) ÷ 4 = - $\frac{3}{2}$ = - 1.5