Question

Solve the equation $3 \mathrm{x}^{2}+5 \mathrm{x}-7=0$

   Solve the equation $3 \mathrm{x}^{2}+5 \mathrm{x}-7=0$

Algebra and Trigonometry

Algebra and Trigonometry

StemEZ 1st Edition

Chapter 17, Problem 484

Instant Answer

Solved by Expert Julia Choi

05/25/2020

Step 1

This is a quadratic equation because it has the form ax^2 + bx + c = 0, where a = 3, b = 5, and c = -7. Show more…

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Solve the equation $3 \mathrm{x}^{2}+5 \mathrm{x}-7=0$

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero. Quadratic equations are fundamental in algebra, and solving them is essential for various applications in mathematics including graphing parabolas, finding maximum or minimum values, and solving geometric problems.

Discriminant

The discriminant is the expression b² - 4ac found under the square root in the quadratic formula. It determines the nature of the roots of a quadratic equation: if the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real repeated root; and if it is negative, the equation has two complex conjugate roots.

Quadratic Formula

The quadratic formula, given by x = (-b ± ?(b² - 4ac)) / (2a), provides a reliable method for solving any quadratic equation. It is particularly useful when the quadratic does not factor easily, ensuring a universal approach to finding the roots, whether they are real or complex.

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