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Use the discriminant to determine the nature of the roots of the following equation. x2 + 2x + 5 = 0 Double root real and rational root real and irrational root non-real root

Respuesta :

mreijepatmat
x² + 2x + 5
Discriminent Δ = b² - 4.a.c

Δ = 4 - 4(1)(5) = -16

since Δ < 0, then  there is non-real roots

To solve the problem we must know about Discriminant.

What is Discriminant?

The part in the formula of a quadratic equation that helps us to know the nature of the roots of a quadratic equation is known as a discriminant.

[tex]\rm{ Discriminant = b^2 -4ac[/tex],

  • If the value of the discriminant is greater than zero then the roots of the equation are real and distinct, [tex]b^2 -4ac >0[/tex]
  • If the value of the discriminant is equal to zero then the roots of the equation are real and same, [tex]b^2 -4ac =0[/tex]and
  • If the value of the discriminant is less than zero then the roots of the equation are no real roots [tex]b^2 -4ac <0[/tex].

The roots of the quadratic equation are not real.

Explanation

Given to us

  • [tex]x^2 + 2x + 5 = 0[/tex]

The values according to quadratic equation,

  • a = 1,
  • b = 2, and
  • c = 5.

Discriminant

Substituting the values in the formula of discriminant,

[tex]\rm{ Discriminant = b^2 -4ac[/tex]

[tex]\rm{ Discriminant = (2)^2 -4(1)(5)[/tex]

                    [tex]= -16[/tex]

Hence, the roots of the quadratic equation are not real.

Learn more about Discriminant:

https://brainly.com/question/15884086

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