Question

Please help ASAP!!!!!!

Answer 1

9514 1404 393

Answer:

  a) correct

  b) needs parentheses: -1, (1±i√2)/3

Step-by-step explanation:

a) You can factor by grouping:

  (x³ -2x²) -(5x -10) = x²(x -2) -5(x -2) = (x² -5)(x -2)

Roots are ±√5, 2.

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b) The sum of odd-degree coefficients is equal to the sum of even-degree coefficients (3-1 = 1+1), so one root is x=-1. Factoring out that leaves the quadratic factor ...

  3x³ +x² -x +1 = (x +1)(3x² -2x +1)

The quadratic formula can be used on the quadratic factor to find its roots:

  x = (-(-2) ±√((-2)²-4(3)(1)))/(2(3)) = (2 ±√-8)/6 = (1 ±√-2)/3

Roots are -1, (1 ±i√2)/3.