Posted by anon on Tuesday, December 20, 2011 at 10:29pm.
solve the inequality express in interval notation
x^4 + 4x^3  9x^2  36x < 0

algebra  Reiny, Wednesday, December 21, 2011 at 9:06am
x(x^3 + 4x^2  9x  36) < 0
x( x^2(x+4)  9(x+4) ) = 0
x(x+4)(x^29) < 0
x(x+4)(x+3)(x3) < 0
so your critical values are
x = 0, 3, 4, and 3
Knowing that y = x^4 + .... is a quartic that rises in the 1st and 2nd quadrant because of the +1x^4 term, and it has 4 xintercepts, you can make a rough sketch showing a W shape with those intercepts.
It should be obvious that the graph is below the xaxis ( y < 0 ) for values between 3 and 4 or between 0 and 3
so in standard notation:
4 < x < 3 OR 0 < x < 3
I will leave it up to you to express it in interval notation

algebra  anon, Wednesday, December 21, 2011 at 10:36am
Thank you!
Answer This Question
Related Questions
 Alegra  solve the inequality express in interval notation x^4 + 4x^3  9x^2  ...
 Solve Inequality  Solve the inequality. Express your solution using interval ...
 math/algebra  Solve the polynomial inequality and graph the solution set on a ...
 algebra  Solve the polynomial inequality and graph the solution set on a real ...
 Algebra  Solve the polynomial inequality and graph the solution set on a real ...
 Math Homework  Solve the inequality and express the answer in interval notation...
 pre cal  solve the inequality express your solution in interval notation (x  4...
 Math  Solve the inequality by first rewriting it as an equivalent inequality ...
 precalculus  solve the inequality express your solution using interval notation...
 algebra  solve the inequality. Express the solution using interval notation and...
More Related Questions