Question

Solve by using the Quadratic Formula. $2 p^{2}-7 p+3=0$

   Solve by using the Quadratic Formula.
 $2 p^{2}-7 p+3=0$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 10, Problem 101

Instant Answer

Solved by Expert Marc Lauzon

07/17/2021

Step 1

In the equation $2p^{2}-7p+3=0$, we have $a=2$, $b=-7$, and $c=3$. Show more…

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Solve by using the Quadratic Formula. $2 p^{2}-7 p+3=0$

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Key Concepts

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a method used to solve quadratic equations. It is derived by completing the square on the general form of a quadratic equation and provides a systematic approach to finding the exact solutions regardless of whether the equation can be easily factored.

Discriminant

The discriminant is the part of the quadratic formula given by b² - 4ac. It determines the nature and number of the roots of the quadratic equation. A positive discriminant implies two distinct real roots, zero indicates one real repeated root, and a negative discriminant results in two complex conjugate roots.

Coefficients

The coefficients in a quadratic equation (commonly represented as a, b, and c) indicate the multipliers of the quadratic term, the linear term, and the constant term respectively. Understanding these coefficients is essential because they are substituted directly into formulas, such as the quadratic formula, to find the roots.

Quadratic Equation

A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. It represents a polynomial of degree 2 and is one of the core topics in algebra, often leading to two solutions or roots when solved.

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