algebra review help?

Question

For some reason I am having trouble with these two algebra review problems for my calculus class, can anyone point me in the right direction?

x^3 - 10x^2 +24x = 0

x^(3/2) - 10x^(1/2) = 0

Thanks in advance

Answer 1

For the first one, you can factor out an x:
x(x^2 - 10x + 24) = 0

Then you want to find two numbers that multiplied make 24, and added make -10. These numbers are -6 and -4. So:
x(x - 6)(x - 4) = 0.
So x = 0, x - 6 = 0, or x - 4 = 0.
x = 0, 6, or 4.


As for the other one: you can factor out x^(1/2) from each one.
(x^(1/2)) * (x - 10) = 0.

So x^(1/2) = 0 or x - 10 = 0.
x = 0 or x = 10.

Answer 2

for the first problem factor out an x. This leaves you with x(x^2-10x+24) = 0
Then factor whats in parentheses.

For the second problem, factor out an x^(1/2).
This leaves you with x^1/2(x-10) = 0
Then set each piece equal to zero

Hope that helps. Let me know if you need anything else.

Answer 3

x³ - 10x² +24x = 0
x(x² - 10x + 24) = 0
D = -10² - 4.1.24
D = 100 - 96
D = 4
x '"= 0
x = (10 +/-\/4):2
x' = (10 + 2):2
x' = 12/2 = 6
x" = (10-2): 2
x" = 8/2 = 4
x' = 6; x" = 4; x'" = 0
<>
x^(3/2) - 10x^(1/2) = 0

x³/² = \/x³ = x\/x
10x¹/² = \/10
So:
x\/x - \/10 = 0
x\/x = \/10
x = \/10 over \/x
x = \/10 * \/x over (\/x)²
x = sqrt of (10x) over x
or
x = \/10x/x
<>

Answer 4

x(x^2 - 10x + 24) = 0

x(x-6)(X-4) = 0

X = 0, 4, 6

X^3/2 - 10x^1/2 = 0

x^1/2(x - 10) = 0

x = 0, 10

Answer 5

the right ( and only direction ) is to notice that
x=0 is a solution ( in both cases )

case 1)
next divide one x away
you problem is now reduced to a quadratic equation

case 2)
divide x^1/2 away
you problem is now reduced to a quadratic equation

Answer 6

3(5v+a million/3) - 4 = 7 +4 = +4 identity sources 3(5v+a million/3) = 11 15v + a million =11 communicative sources (bigger with the aid of with the aid of 3) -a million = -a million identity sources (subtracted a million from the two factors) 15v = 10 15v/15 = 10/15 identity sources (divided the two factors with the aid of 15) v = 2/3