Chapter 9: Q22. (page 595)

Find the two numbers that have a sum of 2 and a product of $- 15$ .

Short Answer

Expert verified

The two numbers are $- 3$ and 5.

Step by step solution

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

The standard form of the quadratic equation is given by

$a x^{2} + b x + c = 0$ Where, $a \neq 0$ .

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 $- 15$ .

Therefore,

role="math" localid="1647869395507" $x (2 - x) = - 15 2 x - x^{2} = - 15 x^{2} - 2 x - 15 = 0$

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

Split the mid-term to solve the equation $x^{2} - 2 x - 15 = 0$ .

role="math" localid="1647869538451" $x^{2} - 5 x + 3 x - 15 = 0 x (x - 5) + 3 (x - 5) = 0 (x - 5) (x + 3) = 0 x = - 3, 5$

Now at, $x = - 3$

The second number $= 2 - (- 3) = 2 + 3 = 5$

Now at $x = 5$

The second number $= 2 - 5 = - 3$

So, the two numbers can be $- 3$ and 5.

Therefore, the two numbers are $- 3$ and 5.

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Number of Tickets	Prize Category
$1 - 20$	bronze
$21 - 40$	silver
$41 - 60$	gold
$61 - 80$	platinum

Find the two numbers that have a sum of 2 and a product of $- 15$ .

Short Answer

Step by step solution

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

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

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

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

Short Answer

Step by step solution

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the two numbers that have a sum of 2 and a product of $- 15$ .