staciethompson11364: What are the roots of the quadratic equation x2 - 19x + 84 = 0?
I like Serena is absolutely correct but i want to talk about how he got his answer.
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What are the roots of the quadratic equation x
2 - 19x + 84 = 0?
You have to look for 2 numbers that multiply to give 84 and add to give -19
Since they muliply to give a positive number than they both must have the same sign. Both pos OR both neg
BUT these two numbers have to add to give a negative number so they both must be negative.
Lets look at factors of 84
-2 and -42 ? No they don't add to -19
-12 and -7 ? yes, they add to -19 so they are the numbers that you need.
So we have found that the factors are (x-12) and (x-7) that is
(x-12)(x-7)=0
Now, if two things multiply together to give you zero, then one of them has to equal 0 (or maybe both) therfore,
either x-12=0 or x-7=0
when you solve these little equations you get x=12 or x=7
+135 
+118654 
