SOLUTION: HELP!!! Determine the values of the variable for which the expression is defined as a real number(answer in interval notation)?
1. Sqrt of 5(x)^2 -7x+2
2. (x)^5 +(x)^3 great
Algebra.Com
Question 1039273: HELP!!! Determine the values of the variable for which the expression is defined as a real number(answer in interval notation)?
1. Sqrt of 5(x)^2 -7x+2
2. (x)^5 +(x)^3 greater or equal to (x)^2 +5x. (Interval notation rounded to two decimals).
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the first is where 5x^2-7x+2>=0
(5x-2)(x-1)> = 0
the roots are x=(2/5) and x=1
Between these, the value is <0
so the intervals are(-oo,2/5] and [1,oo)
================
x^5+x^3>=x^2+5x
x^5+x^3-x^2-5x>=0.
This is <0 when x <-1.23
It is >=0 when x is between -1.23 and 0
It is <0 when x is between (0,1.44)
It is >0 when x>=1.44
[-1.23,0]U[1.44,oo]
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine the values of the variable for which the expression is defined as a real number(answer in interval notation)?
1. Sqrt of 5(x)^2 -7x+2
Solve:: 5x^2-7x+2 >= 0
(5x-2)(x-1) >= 0
Draw a number line and plot x = 2/5 and x = 1
Find the solution intervals::
For x <= 2/5:: -*- > 0 ; true ; solutions in (-oo,2/5]
for 2/5< x <1:: +*- > 0; false ; no solutions in (2/5,1)
for 1 <= x <+oo:: +*+ >0 true ; solutions in [1,+oo)
------------------------------------------------------------
2. (x)^5 +(x)^3 greater or equal to (x)^2 +5x. (Interval notation rounded to two decimal places).
x^5+x^3-x^2-5x >= 0
x[x^4+x^2-x-5] >= 0
Solve x^4+x^2-x-5 >=0
x = -1.23 or x = 1.44
Solutions::
For -oo 0 ; false ; no solutions in (-oo,-1.23)
For -1.23<= x <0 ;; -*- > 0 ; true ; solutions in [-1.23,0]
For 0< x < 1.44 :: +*- > 0 ; false ; no solutions in (0,1.44)
For 1.44<= x <+oo :: +*+ > 0 ; true ; solutions in [1.44,+oo
-----------------
Cheers,
Stan H.
-------------------
RELATED QUESTIONS
Someone please help me with this.
Determine the values of the variable for which the... (answered by KMST)
Determine the values of the variable for which the expression is defined as a real... (answered by stanbon,ikleyn)
Determine the values of the variable for which the expression is defined as a real... (answered by jsmallt9)
Determine the values of the variable for which the expression is defined as a real... (answered by ikleyn)
Determine the value or values of the variable for which the expression is defined.... (answered by ikleyn)
For what values of x is the expression sqrt(4x-x^2) defined as a real... (answered by checkley77)
For what values of x is the algebraic expression defined as a real number?... (answered by edjones)
can you please help me solve the question:
determeine the vales for the variables... (answered by chitra)
Help Please ! Determine the value or values of the variable for which
x-6/x^2-7x+12 is (answered by ewatrrr)