Question

Which of the following are solutions to the quadratic equation? Check all that

Answer 1

Answer:

{-2, 1/3)

Step-by-step explanation:

Combine like terms in 2x2 + 7x - 2 =- x2 + 2x:  We get:

3x^2 + 5x - 2 = 0

Use synthetic division from this point on.  If the remainder in synthetic division is zero, the divisor is a root of the polynomial.  Setting up this division for the possible root 3, we get:

 3     /    3     5     -2

                    15    60

        ----------------------

             3      20   58    The non-zero remainder tells us that 3 is NOT a

                                      solution.

Try C:  x = -2.  Is this a solution?

-2     /    3     5     -2

                    -6      2

        ----------------------

             3      -1       0    The zero remainder tells us that -2 is a solution (C)

The other factor is (3x - 1).  If we set this equal to zero and solve for x, we get:

3x = 1, or x = 1/3.  Thus B:  1/3 is the second solution.                                  

Answer 2

Answer:

x = 1/3 or -2

Step-by-step explanation:

2x^2 + 7x - 2 = - x^2 + 2x

3x^2 + 5x - 2 = 0 (use factoring)

(3x − 1)(x + 2) = 0

3x - 1 = 0    OR     x + 2 = 0

3x = 1                   x = - 2

x = 1/3

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