Find two numbers whose product is -140 and sum is -4.

\left\{\begin{array}{ccc}x\cdot y=-140\\x+y=-4& y=-x-4\end{array}\right\\\\substitute:\\\\x\cdot(-x-4)=-140\\-x^2-4x+140=0\\\\\Delta=(-4)^2-4\cdot(-1)+140=16+560=576;\ \sqrt\Delta=\sqrt{576}=24\\\\x_1=\frac{4-24}{2\cdot(-1})=\frac{-20}{-2}=10;\ x_2=\frac{4+24}{2\cdot(-1)}=\frac{28}{-2}=-14\\\\y_1=-10-4=-14;\ y_2=-(-14)-4=14-4=10\\\\Answer:10\ and\ -14.

Answered by Anonymous | 2024-06-10

{xy=-140, x+y+4=0) (xy=-140, y=-x-4) x=10, y=-14 x=-14, y=10

Answered by socrates990 | 2024-06-10

The two numbers whose product is -140 and sum is -4 are 10 and -14. We determined these numbers by setting up equations based on their product and sum. Using the quadratic formula, we solved for the numbers step-by-step.
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Answered by Anonymous | 2024-09-30