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Chapter 6: Problem 88

What is a quadratic equation?

Short Answer

Expert verified
A quadratic equation is a second-order polynomial equation in a single variable x, with a nonzero coefficient for the x虏 term. It is generally in the form \( ax^2 + bx + c = 0 \). The solutions are calculated using the quadratic formula.

Step by step solution

01

Define Quadratic Equation

A quadratic equation is a second-order polynomial equation in a single variable x, with a nonzero coefficient for the x虏 term. In other words, it has to include a term with x虏.
02

Explain the Structure of a Quadratic Equation

It generally takes the form \( ax^2 + bx + c = 0 \) where \( a 鈮� 0 \). The coordinates x that satisfy this equation are called solutions or roots.
03

Explain the Components of a Quadratic Equation

In the formula \( ax虏 + bx + c = 0 \), \(a\), \(b\), and \(c\) are coefficients. Here, \(a\) is the coefficient of \(x^2\), \(b\) is the coefficient of \(x\), and \(c\) is the constant term. The solutions/roots of the equation are calculated using the quadratic formula, which is derived from the process of completing the square.

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Most popular questions from this chapter

Solve equation and check your solutions. \((x-3)^{2}+2(x-3)-8=0\)

The length of a rectangular garden is 5 feet greater than the width. The area of the rectangle is 300 square feet. Find the length and the width.

Use factoring to solve quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\)-intercepts. \(x(3 x+8)=-5\)

Use the \(x\)-intercepts for the graph in \(a[-10,10,1]\) by \([-13,10,1]\) viewing rectangle to solve the quadratic equation. Check by substitution. Use the graph of \(y=x^{2}+x-6\) to solve \(x^{2}+x-6=0\).

In Exercises \(137-141,\) factor completely. $$5 y^{5}-5 y^{4}-20 y^{3}+20 y^{2}$$
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