Home » Find the roots of x(^3) – 2x(^2) – 5x + 6 = 0

Find the roots of x(^3) – 2x(^2) – 5x + 6 = 0

Find the roots of x(^3) – 2x(^2) – 5x + 6 = 0

  • A.
    1, -2, 3
  • B.
    1, 2, -3,
  • C.
    -1, -2, 3
  • D.
    -1, 2, -3
Correct Answer: Option A
Explanation

Equation: x(^3) – 2x(^2) – 5x + 6 = 0.

First, bring out a(_n) which is the coefficient of x(^3) = 1.

Then, a(_0) which is the coefficient void of x = 6.

The factors of a(_n) = 1; The factors of a(_0) = 1, 2, 3 and 6.

The numbers to test for the roots are (pm (frac{a_0}{a_n})).

= (pm (1, 2, 3, 6)).

Test for +1: 1(^3) – 2(1(^2)) – 5(1) + 6 = 1 – 2 – 5 + 6 = 0.

Therefore x = 1 is a root of the equation.

Using long division method, (frac{x^3 – 2x^2 – 5x + 6}{x – 1}) = x(^2) – x – 6.

x(^2) – x – 6 = (x – 3)(x + 2).

x = -2, 3.

(therefore) The roots of the equation = 1, -2 and 3.

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