solve the inequality express in interval notation
x^4 + 4x^3 - 9x^2 - 36x < 0
5 answers
Assistance needed.
Ah yeah which is why I post the question.
Alissa -- Writeacher corrected your spelling of "Algebra" so that a math expert would see your post.
Jiskha doesn't have any experts in Alegra (whatever that is).
Jiskha doesn't have any experts in Alegra (whatever that is).
x^4 + 4x^3 - 9x^2 - 36x
= x(x^3 + 4x^2 - 9x - 36)
Cubics are hard to solve, so look for easy roots. They will be factors of 36.
A little synthetic division reveals
(x+4)(x+3)x(x-3)
Now since everything is single roots, the graph alternates between positive and negative between roots.
Since it's a quartic with a positive coefficient, it will be positive before the lowest root and after the highest root.
So,
y > 0 for x < -4
y < 0 for -4 < x < -3
y > 0 for -3 < x < 0
y < 0 for 0 < x < 3
y > 0 for x > 3
= x(x^3 + 4x^2 - 9x - 36)
Cubics are hard to solve, so look for easy roots. They will be factors of 36.
A little synthetic division reveals
(x+4)(x+3)x(x-3)
Now since everything is single roots, the graph alternates between positive and negative between roots.
Since it's a quartic with a positive coefficient, it will be positive before the lowest root and after the highest root.
So,
y > 0 for x < -4
y < 0 for -4 < x < -3
y > 0 for -3 < x < 0
y < 0 for 0 < x < 3
y > 0 for x > 3
Thank you I appreciate your help and the fact that you didn't make a big issue out of a typo. Again thank you.
2 answers