Question

write two numbers that multiply to the value on top and add to the value on bottom. -8 +× 15 answer attempt 1 out of 2

Explanation:

Step1: Set up equations

Let the two numbers be $x$ and $y$. We know that $xy = 15$ and $x + y=- 8$. From $x + y=-8$, we have $y=-8 - x$.

Step2: Substitute and solve quadratic - equation

Substitute $y=-8 - x$ into $xy = 15$, we get $x(-8 - x)=15$. Expand to $-8x-x^{2}=15$, or $x^{2}+8x + 15 = 0$. Factor the quadratic equation: $(x + 3)(x + 5)=0$.

Step3: Find the values of $x$ and $y$

Set each factor equal to zero: $x+3 = 0$ gives $x=-3$, and $x + 5=0$ gives $x=-5$. When $x=-3$, $y=-5$; when $x=-5$, $y=-3$.

Answer:

• 3 and - 5