Question

Solve each equation using the Quadratic Formula. $$ 2 x^{2}=7 x-8 $$

   Solve each equation using the Quadratic Formula. 
$$
2 x^{2}=7 x-8
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 20

Instant Answer

Solved by Expert Amrita Bhasin

08/08/2019

Step 1

So, we rewrite the given equation $2x^2 = 7x - 8$ as $2x^2 - 7x + 8 = 0$. Here, $a = 2$, $b = -7$, and $c = 8$. Show more…

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Solve each equation using the Quadratic Formula. $$ 2 x^{2}=7 x-8 $$

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Key Concepts

Discriminant

The discriminant, calculated as b² - 4ac, is a key component of the quadratic formula. It determines the nature and number of the roots: if the discriminant is positive, there are two distinct real roots; if it is zero, there is one repeated real root; and if it is negative, the equation has two complex roots.

Quadratic Formula

The quadratic formula, given by x = (-b ± ?(b² - 4ac)) / (2a), is a universal method for solving quadratic equations that have been written in standard form. It works for all quadratic equations and provides the roots directly by substituting in the values of a, b, and c.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable. Its general form is ax² + bx + c = 0, where a, b, and c are constants and a is not zero. Quadratic equations are fundamental in algebra, and they often represent parabolic curves in coordinate geometry.

Standard Form

Converting an equation to standard form involves rearranging it so all terms are on one side of the equality, setting the expression equal to zero. This standardization is crucial because it provides the proper structure required to apply solution methods like the quadratic formula.

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