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

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Question 382761: Find two numbers such that their sum is 10 and their product is 22?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let p, q be two roots of a monic quadratic polynomial x%5E2+%2B+bx+%2B+c+=+0 (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
x%5E2+-+10x+%2B+22+=+0 which we can find the roots p, q. By the quadratic formula,
p, q = %2810+%2B-+sqrt%2812%29%29%2F2+=+5+%2B-+sqrt%283%29
Therefore the two numbers are 5+%2B+sqrt%283%29 and 5+-+sqrt%283%29.