two numbers whose sum is 3 and whose product is -28

Question

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Answer 1

If a and b are the numbers then a+b=3 and ab=-28. We can write b=3-a and substitute this into the product:

a(3-a)=-28, so 3a-a^2=-28 and a^2-3a-28=0=(a+4)(a-7), from which a=-4 or 7. This means b=7 or -4 so the two numbers are -4 and 7.