Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is the discriminant of $x^2+2x+8=0$ and what does that mean?

1 Answer

Jul 15, 2015

The discriminant of $x^2+2x+8 = 0$ is $(-28)$ which means that this equation has no Real solutions.

Explanation:

For a quadratic equation in the form
$color(white)("XXXX")$ $ax^2+bx+c=0$
the discriminant is
$color(white)("XXXX")$ $Delta = b^2-4ac$

The discriminant is the portion of the quadratic formula for solving a quadratic equation:
$color(white)("XXXX")$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

Seen in this context, it should be clear why:
$color(white)("XXXX")$ $Delta { ( > 0, rarr, 2 " Real solutions"), (=0,rarr, 1 " Real solution"), (< 0, rarr, " no Real solutions"):}$

For the given quadratic
$color(white)("XXXX")$ $x^2+2x+8 = 0$
the discriminant is
$color(white)("XXXX")$ $Delta = 2^2 - 4(1)(8) = -28$
which tells us that this equation has no Real solutions.

Related questions

See all questions in Solutions Using the Discriminant

Impact of this question

8009 views around the world

You can reuse this answer
Creative Commons License