Question 638427: How would I solve these inequalities by factoring and making appropriate sign charts?
1. x^2 - 3x >= 10
or
2. x^3 + 4x^2 - x >= 4
or
3. 2sin^2(x)>= sinx , 0<=z<=2pi
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve these inequalities by factoring and making appropriate sign charts?
1. x^2 - 3x >= 10
x^2-3x-10 >= 0
Factor:
(x-5)(x+2)>= 0
---
Draw a number line ; plot x = -2 and x = 5
If x<-2 the product is > 0
If -2< x <5 the product is < 0
If x > 5 the product is > 0
----
Solution: (-oo,-2]U[5,+oo)
===============================
or
2. x^3 + 4x^2 - x >= 4
x^3+4x^2-x-4 >=0
x^2(x+4)-(x+4)>= 0
(x+4)(x^2-1)>=0
(x-1)(x+1)(x+4) >= 0
Draw a number line ; plot x = -4, x = -1, x = +1
---
Find the solution intervals.
=====================================
or
3. 2sin^2(x)>= sinx , 0<=z<=2pi
2sin^2(x)-sin(x) >= 0
sin(x)(2sin(x)-1) >= 0
sin(x) = 0 , sin(x) = 1/2
Draw a number line ; plot x = 0, x = pi/6, x = (5/6)pi, x = 2pi
----
Find the solution intervals.
=================================
Cheers,
Stan H.
=================
|
|
|
