Question

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

Answer 1

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 $i = \sqrt{-1}$. The two solutions are different from one another.

Answer 2

Answer:

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

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

In $x^2+3x+8$, assign:

• $a\implies 1$
• $b\implies 3$
• $c\implies 8$  

The discriminant is therefore:

$3^2-4(1)(8)=9-32=\boxed{-23}$

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.