## Who invented the fundamental theorem of algebra?

Carl Friedrich Gauss

fundamental theorem of algebra, Theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

**What is the fundamental theorem in algebra?**

: a theorem in algebra: every equation which can be put in the form with zero on one side of the equal-sign and a polynomial of degree greater than or equal to one with real or complex coefficients on the other has at least one root which is a real or complex number.

**Why Is Fundamental Theorem of Algebra important?**

The Fundamental Theorem of Algebra tells us that every polynomial function has at least one complex zero. This theorem forms the foundation for solving polynomial equations.

### Who proved the fundamental theorem of algebra in 1799?

Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral disser- tation. However, Gauss’s proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss’s proof.

**How did Gauss prove?**

His doctoral thesis of 1797 gave a proof of the fundamental theorem of algebra: every polynomial equation with real or complex coefficients has as many roots (solutions) as its degree (the highest power of the variable). Gauss’s proof, though not wholly convincing, was remarkable for its critique of earlier attempts.

**Who discovered the Descartes rule *?**

Descartes’ Rule of Signs is a useful and straightforward rule to determine the number of positive and negative zeros of a polynomial with real coefficients. It was discovered by the famous French mathematician Rene Descartes during the 17th century.

#### How do you prove the fundamental theorem of algebra?

Proof: If α is a real or complex root of the polynomial p(z) of degree n with real or complex coefficients, then by dividing this polynomial by (z–α) , using the well-known polynomial division process, one obtains p(z)=(z–α)q(z)+r p ( z ) = ( z – α ) q ( z ) + r , where q(z) has degree n–1 and r is a constant.

**What is the fundamental theorem of algebra Quizizz?**

Q. Which formula is the Fundamental Theorem of Algebra Formula? There are infinitely many rationals between two reals. Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

**What is history of algebra?**

The word “algebra” is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation …

## Who discovered Gauss law?

The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1835, both in the context of the attraction of ellipsoids. It is one of Maxwell’s four equations, which forms the basis of classical electrodynamics. Gauss’s law can be used to derive Coulomb’s law, and vice versa.

**What does Descartes rule say?**

Descartes’ rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.

**What are real roots?**

The real roots are expressed as real numbers. Suppose ax2 + bx + c = 0 is a quadratic equation and D = b2 – 4ac is the discriminant of the equation such that: If D = 0, then the roots of the equation are real and equal numbers. If D > 0, then the roots are real and unequal.