What is the value of discriminant (b² – 4ac) for the equation 5x² + 7x + 6?

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To determine the value of the discriminant for the quadratic equation in the form:

ax² + bx + c = 0

we need to identify the coefficients a, b, and c from the given equation 5x² + 7x + 6 = 0.

  1. a: The coefficient of x² is 5.
  2. b: The coefficient of x is 7.
  3. c: The constant term is 6.

Now that we have identified the coefficients, we can substitute them into the discriminant formula:

D = b² – 4ac

Substituting in the values:

D = (7)² – 4(5)(6)

Calculating 7² gives us 49:

D = 49 – 4(5)(6)

Now calculating the value of 4(5)(6):

4 * 5 = 20

20 * 6 = 120

So we have:

D = 49 – 120

Finally, when we subtract 120 from 49, we get:

D = -71

The negative discriminant indicates that the quadratic equation has no real roots but has two complex roots. Therefore, the value of b² – 4ac for the equation 5x² + 7x + 6 is -71.

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