/*! 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} Problem 73 Use the Quadratic Formula to sol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 73

Use the Quadratic Formula to solve the quadratic equation. $$4 x^{2}+16 x+17=0$$

Short Answer

Expert verified
The solutions of the quadratic equation \(4x^2 + 16x + 17 = 0\) are x = -2 + 0.5i and x = -2 - 0.5i

Step by step solution

01

Identify a, b and c

In the equation \(4x^2 + 16x + 17 = 0\), a=4, b=16 and c=17. The coefficients a, b and c are always extracted from the equation in its standard form.
02

Substitute the values of a, b and c in the quadratic formula

In the quadratic formula \(x = [-b 卤 sqrt(b ^ 2 - 4ac)] / 2a\), replace a, b, and c with 4, 16 and 17 respectively to get \(x = [-16 卤 sqrt((16) ^ 2 - 4 * 4 * 17)] / 2 * 4\)
03

Simplify the expression

Simplify the expression under the square root and the denominator to get \(x = [-16 卤 sqrt(256 - 272)] / 8 = [-16 卤 sqrt(-16)] / 8\)
04

Solve for x

As the value under the square root is negative, the solutions are complex. Taking square root of -16 gives 4i. So, the solutions are \[x = -16 / 8 卤 4i / 8 = -2 \pm 0.5i\]

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

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=4 x^{2}-8 x+3$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{3}-x+6$$

Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) $$2,5+i$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$f(x)=4 x^{3}-3 x^{2}+2 x-1$$

Decide whether the statement is true or false. Justify your answer. It is possible for a third-degree polynomial function with integer coefficients to have no real zeros.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.