Destroyer QR Question 25...

[BalooTheBear]

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I was wondering if someone could explain this to me. I tried searching for old posts, but nothing came up for this question:

#25 Find the roots of 2x^2-10x+12=0

Apparently, the answer is x=3 and x=2. It says to divide both sides by 2 and then solve normally (from x^2-5x+6=0)

I solved it my way (the wrong way) and found x=-1 and x=6. Anyone else get that?
Maybe I've missed this topic, but why was everything divided by 2 when it asked for the "roots"?

I tried searching other books and even google, but it was hard to find something for this specific question.
Any insight would be amazing. Thank you

 

[nwdmd]

2x^2 - 10x + 12 = 0
factor out 2 (distributive property)
2 (x^2 - 5x + 6) = 0

this is similar to dividing both sides by 2 to "remove" 2, which is only acceptable in this problem because we're just worried about what values of x lead to zero. It's not necessary, just speeds up the polynomial factoring.

factor out the polynomial:
2(x - 2)(x - 3) = 0

x - 2 = 0 ; x = 2
x - 3 = 0 ; x = 3

hopefully this helps, i think dividing both sides by 2 led to the confusion?

 

[BalooTheBear]

wow......totally see what you mean, can't believe i missed that...maybe staying up late isn't the best thing to do...thanks for your help