Chapter 9.3, Problem 35PPS

To determine

To obtain a quadratic equation and fine the two numbers.

Answer to Problem 35PPS

The two numbers are -3 and 4 .

Explanation of Solution

Given information :

The sum of the two numbers is 1 and their product is -12 .

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 .

  $x+y=1$

Sum of the numbers.

  $x=1-y$

Rearranging x and y. Let this be equation 1.

  $x\times y=-12$

Product of the numbers. Let this be equation 2.

  $=>\left(1-y\right)\times y=-12$

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

  $=>y-y^2=-12$

This can be arranged as

  $=>y^2-y-12=0$

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

  $=>y^2-4y+3y-12=0$

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

  $=>y\left(y-4\right)+3\left(y-4\right)=0$

Arranging the common elements.

  $=>\left(y-4\right)\left(y+3\right)=0$

These are the factors.

Hence the given numbers are -3 and 4 .