SOLUTION: Find two numbers such that their sum is 10 and their product is 22?

Question 382761: Find two numbers such that their sum is 10 and their product is 22?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let p, q be two roots of a monic quadratic polynomial (without loss of generality assume the x^2 coefficient 1).
By Vieta's formulas, the sum of the roots is -b, and p + q = -b, so b = -10. Also, the product of the roots is c, i.e. pq = 22 --> c = 22. Therefore we have established our polynomial
which we can find the roots p, q. By the quadratic formula,
p, q =
Therefore the two numbers are and .
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