Question

Solve each equation. See Example 3 . $$ 4 a^{2}+4 a+5=0 $$

   Solve each equation. See Example 3 .
$$
4 a^{2}+4 a+5=0
$$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 8, Problem 35

Instant Answer

Solved by Expert Cory Kuzinski

08/03/2020

Step 1

Here, $a = 4$, $b = 4$, and $c = 5$. Show more…

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Solve each equation. See Example 3 . $$ 4 a^{2}+4 a+5=0 $$

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in a single variable, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a is nonzero. This type of equation is fundamental in algebra and appears in various problems across mathematics and applied sciences.

Quadratic Formula

The quadratic formula is a method for finding the roots of any quadratic equation. It is given by x = (-b ± ?(b² - 4ac)) / (2a), and it provides a straightforward way to compute the solutions, regardless of whether the roots are real or complex.

Discriminant

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

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