/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q13. NUMBER THEORY Use a quadratic eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q13. (page 297)

NUMBER THEORY Use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

Short Answer

Expert verified

The numbers are -2 and 7.

Step by step solution

01

Step-1 – Given

The sum = 5 and product = -14.

02

Step-2 – To determine

Use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

03

Step-3 – Calculation

Let the numbers are x and y.

So, the sum is x+y=5and product is xy=-14.

From x+y=5we get, y=5-x

Then we plug it in xy=-14and solve.

xy=鈭�14x(5鈭�x)=鈭�145x鈭�x2=鈭�14x2鈭�5x鈭�14=0x2鈭�7x+2x鈭�14=0x(x鈭�7)+2(x鈭�7)=0(x鈭�7)(x+2)=0x=7,鈭�2

For ,y=5鈭�x=5鈭�7=鈭�2

For , .y=5鈭�x=5鈭�(鈭�2)=5+2=7

So, the numbers are -2 and 7.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=7x2+4x+1

Simplify

4-3i-5-6i

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=3x2

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.
  4. f(x)=-4x2

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

x2-2x-1=0
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.