Respuesta :

joseaaronlara

Answer:

The answer to your question is x = 4

Step-by-step explanation:

                                   2x² - bx - 20 = 0

One root is -2.5

Process

Get the value of the equation when x = -2.5

                                   2(-2.5)² - b(-2.5) - 20 = 0

                                   2(6.25) + 2.5b  - 20 = 0

                                   12.5 + 2.5b - 20 = 0

                                   2.5b = 20 - 12.5

                                   2.5b = 7.5

                                   b = 7.5 / 2.5

                                  b = 3

Then

                                  2x² - 3x - 20 = 0

Factor the polynomial

                                  2 x -20 = -40

                                  2x² -8x + 5x - 20 = 0

                                  2x(x - 4) + 5(x - 4) = 0

                                  (x - 4)(2x + 5) = 0

                                  x₁ - 4 = 0               2x₂ + 5 = 0

                                 x₁ = 4                     x₂ = -5/2

                                                               x₂ = -2.5

                                                             

                               

altavistard

Answer:

The "other" or "second" root is 4.

Step-by-step explanation:

We are told that -2.5 is a root of the equation.  The coefficient b of the x term is unknown, and must be determined.  Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.

Setting up synthetic division, we arrive at:

-2.5    /    2    -b    -20

                     -5     +12.5 + 2.5b

          -------------------------------------

                2   -5-b    -7.5 + 2.5b

The remainer, -7.5 + 2.5b, must be zero (0).  Thus, 2.5b = 7.5, and b = 3.

Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.

The other factor is 2x - 8, which, if set equal to 0, yields x = 4.  This is the "other root."

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