Find two numbers whose sum is 7 and product is -30?

Answer 1

37

Answer 2

Let the numbers be a,b : Then ab = -30 and b = -30/a : Substituting in a + b = 7 gives :-

a + (-30/a) = 7 : a - 30/a = 7 : multiplying all terms by a :-

a2 - 30 = 7a : a2 - 7a - 30 = 0

Solving for the roots of a quadratic equation.

a = {7 ± √(72 - [4 x -30])} ÷ 2 = 3.5 ± 6.5

Then a = 10 (3.5 + 6.5) and b = -3 (3.5 - 6.5)

Answer 3

37 and 37