Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve $3x^2+5x=0$ using the quadratic formula?

2 Answers

Aug 26, 2015

$x=0$
or
$x=-5/3$

Explanation:

Standard quadratic form:
$color(white)("XXXX")ax^2+bx+c=0$

Re-writing the given equation in explicit standard form:
$color(white)("XXXX")3x^2+5x+0=0$
with $a=3$ , $b=5$ , and $c=0$

The quadratic formula is
$color(white)("XXXX")x = (-b+-sqrt(b^2-4ac))/(2a)$

which, in this case becomes
$color(white)("XXXX")x = (-5+-sqrt(5^2-4(3)(0)))/(2(3)$

$rArr x= 0 or x=-10/6 = -5/3$

Aug 26, 2015

The solutions are

$color(blue)(x=0$

$color(blue)(x=-5/3$

Explanation:

The equation $3x^2+5x=0$ :
is of the form $color(blue)(ax^2+bx+c=0$ where:

$a=3, b=5, c=0$
(the equation lacks a constant term)

The Discriminant is given by:
$Delta=b^2-4*a*c$
$= (5)^2-(4*3*0)$
$= 25 - 0=25$

The solutions are found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

$x = ((-5)+-sqrt(25))/(2*3) = ((-5+-5))/6$

$x=((-5+5))/6, color(blue)(x=0$

$x=((-5-5))/6, x=-10/6 color(blue)(x=-5/3$

Related questions

See all questions in Quadratic Formula

Impact of this question

17161 views around the world

You can reuse this answer
Creative Commons License