Given the trinomial 2x² + 4x- 2, what is the value of the discriminant?

Solution:

Given, the trinomial is 2x² + 4x - 2

We have to find the value of the discriminant.

Discriminant, D = b² - 4ac

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

So, D = (4)² - 4(2)(-2)

= 16 - 4(-4)

= 16 + 16

= 32

Therefore, the value of the discriminant is 32.

Example:

What is the value of the discriminant for the quadratic equation -3 = -x² + 2x?

Solution:

Given, -3 = -x² + 2x

We have to find the value of the discriminant for the quadratic equation.

Discriminant, D = b² - 4ac

The quadratic equation can be rewritten as

-3 + x² - 2x = 0

x² - 2x - 3 = 0

Here, a = 1, b = -2 and c = -3.

D = (-2)² - 4(1)(-3)

= 4 - 4(-3)

= 4 + 12

= 16

Therefore, the value of the discriminant is 16.