Find the discernment and the numbers of the number of real roots for this equation.
x^2+3x+8=0

 2 distinct complex solutions (ie non real solutions).

Work Shown:

The given equation is in the form ax^2+bx+c = 0, so

a = 1, b = 3, c = 8

Plug those into the formula below to find the discriminant

D = b^2 - 4ac

D = 3^2 - 4(1)(8)

D = -23

The discriminant is negative, so we get two nonreal solutions. The two solutions are complex numbers in the form a+bi, where a & b are real numbers and . The two solutions are different from one another.

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

For a quadratic in standard form , the discriminant is given by .

In , assign:

The discriminant is therefore:

For any quadratic:

Since the quadratic in the question has a discriminant less than 0, there are no real solutions to this quadratic.

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