SOLUTION: hi i need help starting my homework... i need to solve this: 5x(2x-3)=0 thank you in advance!!

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Question 188556: hi i need help starting my homework... i need to solve this:
5x(2x-3)=0 thank you in advance!!
Found 2 solutions by Alan3354, jojo14344:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
hi i need help starting my homework... i need to solve this:
5x(2x-3)=0 thank you in advance!!
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Since the product is 0, either 5x = 0, or (2x-3) = 0
5x = 0
x = 0
---------
2x-3 = 0
2x = 3
x = 3/2

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given:system%285x%282x-3%29%29 ---> 10x%5E2-15x,--> wheresystem%28a=10%2Cb=%28-15%29%2Cc=0%29

Solving for the X-Intercepts:
Disciminant: b%5E2-4ac=-15%5E2-4%2810%29%280%29=225
Then, by Quadratic,
x=%28-%28-15%29%2B-sqrt%28225%29%29%2F%282%2A10%29=%2815%2B-15%29%2F20
x=%2815%2B15%29%2F20=30%2F20=red%281.5%29
x=%2815-15%29%2F20=0%2F20=red%280%29

X-Intercepts, (1.5,0) & (0,0)

Let fx=0 ----> y=10%280%29%5E2-15%280%29=red%280%29

Y-Intercept, (0,0)

For the vertex: x=-b%2F2a=-%28-15%29%2F%282%2A10%29=15%2F20=red%283%2F4%29
For Y, subst. x= 3/4 to the eqn:
y=10%28.75%29%5E2-15%28.75%29=5.625-11.25=red%28-5.625%29

The vertex, (3/4, -5.625)
We'll see the graph:
--->

Thank you,
Jojo