Question

Solve the equations: $z^{2}-2 z+4=0$

   Solve the equations:
$z^{2}-2 z+4=0$

The Chemistry Maths Book

The Chemistry Maths Book

Erich Steiner 2nd Edition

Chapter 8, Problem 10

Instant Answer

Solved by Expert John Nicolle

01/02/2022

Step 1

Step 1: Compute discriminant: Δ = (-2)^2 - 4*1*4 = 4 - 16 = -12. Show more…

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Solve the equations: $z^{2}-2 z+4=0$

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation expressed in the standard form ax² + bx + c = 0. It is fundamental in algebra and has exactly two roots, which may be real or complex depending on the discriminant.

Discriminant

The discriminant of a quadratic equation is the expression b² - 4ac. It is used to determine the nature of the roots: a positive discriminant indicates two distinct real roots, zero indicates one repeated real root, and a negative discriminant indicates two complex conjugate roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), provides a systematic way to find the roots of any quadratic equation. It is derived through the method of completing the square and is applicable regardless of whether the roots are real or complex.

Complex Numbers

Complex numbers extend the real number system by including the imaginary unit i, defined by i² = -1. They are crucial when solving quadratic equations with negative discriminants, as these situations require taking the square root of a negative number, resulting in complex roots.

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