Question

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

Please explain how you got the solution.

20 Points! Thanks!

Answer 1

Answer: One Real Solution

We can Identify the coefficients a, b, and c from your equation because as it says, it is in the format of the quadratic equation ( ax^2 + bx + c = 0 )

a=2,b=-4,c=2

Now we can use the discriminant to determine how many solutions this has using the equation b^2 - 4ac

Once we plug in our coefficients:

(-4)^2 - 4 x 2 x 2

Once we simplify, we get 0.

One real solution.

I hope this helps.

Answer 2

In this case, we first need to simplify the given quadratic equation 2x² - 4x = -2, and to do so, we perform the following simplification steps:

For a quadratic equation of the form ax² + bx + c = 0, the discriminant is calculated using the following formula:

Δ = b² - 4ac

In this case, we have that the equation that we must solve is 2x²-4=-2, which implies that the corresponding coefficients are:

• a = 2
• b = -4
• c = 2

By introducing these values into the formula we get:

Δ = b² - 4ac = (-4)² - 4·(2)·(2) = 0

Therefore, the discriminant for the given quadratic equation is Δ=0=0, which is zero, and indicates that the equation 2x²-4=-2 has only one real root.

We can say: It has a Real solution.