Respuesta :

Answer:  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 [tex]i = \sqrt{-1}[/tex]. The two solutions are different from one another.

Corsaquix

Answer:

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

For a quadratic in standard form [tex]ax^2+bx+c[/tex], the discriminant is given by [tex]b^2-4ac[/tex].

In [tex]x^2+3x+8[/tex], assign:

  • [tex]a\implies 1[/tex]
  • [tex]b\implies 3[/tex]
  • [tex]c\implies 8[/tex]  

The discriminant is therefore:

[tex]3^2-4(1)(8)=9-32=\boxed{-23}[/tex]

For any quadratic:

  • If the discriminant is greater than 0, the quadratic has two real roots
  • If the discriminant is equal to 0, the quadratic has one real root
  • If the discriminant is less than 0, the quadratic as no real roots

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

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