Question

Who proved the quintic equation does not have roots and when?

a) Galois in 1832
b) Abel in 1824
c) Ruffini in 1799
d) Cardano in 1545

Answer 1

Niels Henrik Abel proved in 1824 that general quintic equations cannot be solved by radicals, a result known as Abel's impossibility theorem.

Step-by-step explanation:

The question asks about who proved that a general quintic equation cannot be solved by radicals (i.e., it does not have roots that can be expressed by a combination of addition, subtraction, multiplication, division, and root extraction). The correct answer is b) Abel in 1824. Niels Henrik Abel, a Norwegian mathematician, provided the proof that general polynomial equations of degree five or higher cannot be solved by a radical expression. This result is known as Abel's impossibility theorem. His work was built upon by Évariste Galois, who in 1832, developed a more general theory that not only explained why the quintic cannot be solved by radicals but also established conditions under which certain higher-degree polynomials could be solvable by radicals.