 Suggested languages for you:

Europe

Problem 19

# The $$x$$ co-ordinates of the vertices of a square of unit area are the roots of the equation $$x^{2}-3|x|+2=0$$ and the $$y$$-co-ordinates of the vertices are the roots of the equation $$y^{2}-3 y+2=0$$. Find the vertices of the square.

Expert verified
The vertices of the square are (-1,1), (1,2), (2,1) and (-2,2).
See the step by step solution

## Step 1: Solve the Quadratic Equation for x

Firstly, let's tackle the equation for x, which is $$x^{2}-3|x|+2=0$$. To solve for $$x$$, split the absolute value equation into its positive and negative components. This will yield the two equations $$x^{2}-3x+2=0$$ and $$x^{2}+3x+2=0$$. Solving these two equations will give four x-coordinates of the vertices, which are $$x= -1, 2, 1, -2$$.

## Step 2: Solve the Quadratic Equation for y

The equation for $$y$$ is $$y^{2}-3y+2=0$$. This equation is standard quadratic form and can be simplified by factoring to yield the equation $$(y-2)(y-1) =0$$. Thus the roots or the y-coordinates of the vertices of the square are $$y=1,2$$.

## Step 3: Formulate the vertices of the square

Given that a square has four vertices and each vertex has an x and a y coordinate, we can formulate the vertices by pairing each x-coordinate with each y-coordinate. Doing this will provide the four vertices of the square. They are (-1,1), (2,1), (1,2) and (-2,2).

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features ## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner 