Inequalities?

Question

How can you solve these questions? I will post a few. Please try to solve at least one or one someone hasn't solved. Please also don't tell me to do my homework, I am doing it and don't understand thanks.

1) x^4+9x^2-10 <= 0
2) x^3+x^2-6x > 0
3) (x+3)x^2(x-2)^3 => 0


Thank u.

Answer 1

Rules of the game:
to start with ignore the inequality and just factorise as if it an ordinary =
So on the first one: x^4 + 9x^2 - 10 = 0
(x^2 + 10)(x^2 - 1) = 0
(x^2 + 10)(x - 1) ( x+ 1) =0
the x^2 bracket does not give an answer so it just cuts the x-axis at 1 and -1
So you need to check 3 areas:
x<-1 say x = 2: 16 + 36 - 10 > o so positive
-1 x>1 say x = 2: as above so positive
Back to the question: where is this negative or zero?
From x = -1 to x = 1 inclusive THE ANSWER!

Answer 2

y=(x^2+10)(x^2-1)
=(x^2+10)(x+1)(x-1)
for y <=0 then -1 =< x =<1

x(x^2+x-6)=x(x+3)(x-2)
root = -3, 0, and 2
y>0 when -3 2