How do you solve #x^2+x-6

Question

How do you solve #x^2+x-6<0# using a sign chart?

Chloe Alexander · Accepted Answer

The answer is #x in ] -3,2 [#

Let's factorise the expression,

#x^2+x-6=(x-2)(x+3)#

and let #f(x)=x^2+x-6#

Now we can do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaaa)##2##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x+3##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-2##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#

Therefore,

#f(x)<0#, when #x in ] -3,2 [ #

Elijah Allen · Answer

undefined To solve $x^2+x-6<0$ using a sign chart:

1. Factor the quadratic equation to find its roots: $x^2 + x - 6 = (x - 2)(x + 3)$.
2. Plot the critical points on the number line: $x = -3$ and $x = 2$.
3. Test the intervals between the critical points and beyond them by picking test points and determining the sign of the expression $x^2+x-6$ in those intervals.
4. Analyze the signs in each interval to determine where the expression is less than zero.
5. Finally, express the solution as an interval or union of intervals where the expression is negative.

The solution to $x^2+x-6<0$ using a sign chart is $-3<x<2$.

How do you solve #x^2+x-6&lt;0# using a sign chart?

How do you solve #x^2+x-6<0# using a sign chart?