What is the value of b² – 4ac for the following equation 2x² + 2x + 1 = 0?

To find the value of b² – 4ac, we first need to identify the coefficients a, b, and c from the quadratic equation in the standard form ax² + bx + c = 0.

For the equation 2x² + 2x + 1 = 0:

• a = 2
• b = 2
• c = 1

Now, we’ll calculate b² – 4ac:

b² - 4ac = (2)² - 4(2)(1)

Calculating each component:

• (2)² = 4
• – 4(2)(1) = – 8

So, we have:

4 - 8 = -4

The value of b² – 4ac for the equation 2x² + 2x + 1 = 0 is -4. This indicates that the quadratic equation has no real roots, as the discriminant (b² – 4ac) is negative.