Chapter 9, Problem 45SGR

To determine

To obtain a quadratic equation and fine the two numbers.

Answer to Problem 45SGR

The two numbers are -8 and 6.

Explanation of Solution

Given information :

The sum of the two numbers is -2 and their product is -48 .

Formula used :

Form a quadratic equation by substituting values of the addition and product of the two numbers. Then, solve the given equation to obtain the numbers.

Calculation :

Let the numbers be x and y .

  $x+y=-2$

Sum of the numbers.

  $x=-2-y$

Rearranging x and y. Let this be equation 1.

  $x\times y=-48$

Product of the numbers. Let this be equation 2.

  $=>\left(-2-y\right)\times y=-48$

Substituting the value of x in equation 1 in equation 2.

  $=>-2y-y^2=-48$

This can be arranged as

  $=>y^2+2y-48=0$

This is the quadratic equation. Solve this to get the two numbers.

  $=>y^2+8y-6y-48=0$

Breaking the middle term that when multiplied, provides that values of $a{x}^2\times c$ .

  $=>y\left(y+8\right)-6\left(y+8\right)=0$

Arranging the common elements.

  $=>\left(y-6\right)\left(y+8\right)=0$

These are the factors.

Hence the given numbers are 6 and -8.