Expert: Richard J. Raridon - 9/13/2011

Question
QUESTION: solve: x2-5x+6=0

ANSWER: x^2-5x+6 = (x-2)(x-3) so x = 2,3

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QUESTION: thank you for answer.but sir,can you explain the answer in brief.

Answer
The standard quadratic equation is ax^2+bx+c = 0
There have to be two factors (although they may be identical) (dx+e) and (fx+g).
If you multiply those factors together and compare them to the original equation you will see that df = a and eg = c.  In this case, a=1 and therefore d and f both = 1.  e and g have to be factors of c, in this case, either 1 & 6 or 2 & 3.  They both have to be negative since c is positive.  So the possibilities are (x-1)(x-6) or (x-2)(x-3)