Question

Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2-4x=-2 has

Answer 1

To determine the number and type of solutions for the quadratic equation \( 2x^2 - 4x = -2 \), we first need to rearrange it into standard form, which is \( ax^2 + bx + c = 0 \).

Starting with the given equation:
\[
2x^2 - 4x + 2 = 0
\]

Now we identify the coefficients:
- \( a = 2 \)
- \( b = -4 \)
- \( c = 2 \)

Next, we calculate the discriminant \( D \) using the formula:
\[
D = b^2 - 4ac
\]

Substituting in the values of \( a \), \( b \), and \( c \):
\[
D = (-4)^2 - 4(2)(2)
\]
\[
D = 16 - 16
\]
\[
D = 0
\]

The discriminant \( D \) is 0, which indicates that there is exactly one real solution (also called a double root) for the quadratic equation.

In summary:
- The quadratic equation \( 2x^2 - 4x + 2 = 0 \) has **one real solution** (a double root).