Which of the following are solutions to the quadratic equation? Check all that apply. 2x2 + 7x - 2 =- x2 + 2x
A. 3
B. 1/3
C. -2
D. 1
E. 2
F. -1/2

{-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.                                  

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

go and ask your mom to you