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Chapter 9: Q22. (page 595)

Find the two numbers that have a sum of 2 and a product of 鈭�15.

Short Answer

Expert verified

The two numbers are -3and 5.

Step by step solution

01

Step 1. Define the standard form of the quadratic equation.

The standard form of the quadratic equation is given by

ax2+bx+c=0Where, a鈮�0.

02

Step 2. Form a quadratic equation by using the question.

Let the first number =x

Since, the sum of the two numbers is 2.

So, the second number =2-x

Since, the product of the two numbers is 鈭�15.

Therefore,

role="math" localid="1647869395507" x2鈭�x=鈭�152x鈭�x2=鈭�15x2鈭�2x鈭�15=0

03

Step 3. Solve the equation x2−2x−15=0.

Split the mid-term to solve the equation x2鈭�2x鈭�15=0.

role="math" localid="1647869538451" x2鈭�5x+3x鈭�15=0xx鈭�5+3x鈭�5=0x鈭�5x+3=0x=鈭�3,鈥�5

Now at, x=鈭�3

The second number =2鈭�鈭�3=2+3=5

Now at x=5

The second number =2鈭�5=鈭�3

So, the two numbers can be 鈭�3and 5.

Therefore, the two numbers are鈭�3 and 5.

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Most popular questions from this chapter

Describe how the graph of the functionfx=x2鈭�3 is related to the graph fx=x2.

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

x2+5x+6=0

Find the vertex, the equation of the axis of symmetry, and the y-intercept of the given equation.

y=7x2鈭�28x+14

Consider y=x2鈭�5x+4

Graph the function.

Graph each function. Find the y-intercept, and state the domain and range.

y=3x+1
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