For the quadratic equation - 2 x2 - 3x + 2 = 0, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of the values is in the solution set.

Question

Only x = 1/2 is in the solution set.

Answer 1

To determine whether each of the given values is a solution to the quadratic equation $-2x^2-3x+2=0$, we will substitute each $x$ value into the equation and check if it results in zero.

Here's how it's done for the given quadratic equation:

1. Substitute values into the equation.
2. Check if the equation equals zero.

We will evaluate the equation for the given value $x=\frac{1}{2}$.

Step 1: Substitute $x=\frac{1}{2}$ into the equation.

$$-2{\left(\frac{1}{2}\right)}^2-3\left(\frac{1}{2}\right)+2=0$$

Calculating term by term:

$$=-2\left(\frac{1}{4}\right)-\frac{3}{2}+2$$ $$=-\frac{2}{4}-\frac{3}{2}+2$$ $$=-\frac{1}{2}-\frac{3}{2}+2$$

Now convert $2$ into halves:

$$=-\frac{1}{2}-\frac{3}{2}+\frac{4}{2}$$ $$=-\frac{1+3-4}{2}$$ $$=-\frac{0}{2}=0$$

So, $x=\frac{1}{2}$ is indeed a solution to the equation $-2x^2-3x+2=0$.

Since you've stated that only $x=\frac{1}{2}$ is in the solution set, we can conclude that it is the only value that satisfies the equation.

You would, however, need to check other proposed values (not just $x=\frac{1}{2}$) if you want to complete the table based on additional values provided. If you have those values, please provide them for evaluation.