SOLUTION: how do you solve this kind of problem? i don't understand how to solve them. can you explain? Ex.: Solve each equation. check your solutions 2x(5x-10)=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do you solve this kind of problem? i don't understand how to solve them. can you explain? Ex.: Solve each equation. check your solutions 2x(5x-10)=0      Log On


   

Question 74468This question is from textbook Algebra 1 Integration Applications Connections
: how do you solve this kind of problem? i don't understand how to solve them. can you explain?
Ex.: Solve each equation. check your solutions
2x(5x-10)=0 This question is from textbook Algebra 1 Integration Applications Connections

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28cross%282x%29%285x-10%29%29%2Fcross%282x%29=0Divide both sides by 2x
5x-10=0
5x=10
x=2There's one answer
Go back to the original problem
%282x%2Across%285x-10%29%29%2Fcross%28%285x-10%29%29=0Divide both sides by (5x-10)
2x=0
x=0There's the other answer. The reason why you have 2 answers is because when x is 0 or 2 (notice the or) then the entire equation equals zero. If I plug in x=0 then I get
2%280%29%285%280%29-10%29=0
0%280-10%29=0
0%28-10%29=0
0=0works
2%282%29%285%282%29-10%29=0
4%2810-10%29=0
4%280%29=0
0=0works
So in a general sense if I have
pq=0 then I can set either p or q equal to zero to solve for p and q since 0 times anything is 0.
So the solution is
p=0 or q=0
So the answer is x=0 or x=2
Also, notice if you graph 2x%285x-10%29 the x-intercepts will be x=0 and x=2. These are points when y=0
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%2A%285x-10%29%29+Graph of 2x%285x-10%29