SOLUTION: What are the x factors of this quadratic equation 5x^2+2x+10=0. Any help will be greatly appreciated.

Question 635651: What are the x factors of this quadratic equation 5x^2+2x+10=0.
Any help will be greatly appreciated.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,5,10,25,50
-1,-2,-5,-10,-25,-50

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*50 = 50
2*25 = 50
5*10 = 50
(-1)*(-50) = 50
(-2)*(-25) = 50
(-5)*(-10) = 50

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	50	1+50=51
2	25	2+25=27
5	10	5+10=15
-1	-50	-1+(-50)=-51
-2	-25	-2+(-25)=-27
-5	-10	-5+(-10)=-15

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

So doesn't factor at all (over the rational numbers).

So is prime.

So the best way to solve the original equation is to use the quadratic formula. Let me know if you need help solving using the quadratic formula.

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