Quartic equation facts for kids

A quartic equation is a special type of math problem called a polynomial equation. It's known as a "fourth-degree" equation because the highest power of the unknown number (usually called 'x') in the equation is 4. Think of it like this: if you have x times x times x times x, that's x to the power of 4, or x⁴.

What is a Quartic Equation?

A quartic equation is a mathematical statement where you have different powers of a variable (like x) added or subtracted, and the biggest power is 4. For example, an equation like ax⁴ + bx³ + cx² + dx + e = 0 is a quartic equation. Here, 'a', 'b', 'c', 'd', and 'e' are just numbers, and 'a' cannot be zero.

Understanding Polynomials

A polynomial is a math expression made up of variables and coefficients (numbers) using only addition, subtraction, multiplication, and non-negative whole number exponents. It's like a chain of terms.

• A simple example is 3x + 2 (a linear polynomial).
• Another is 2x² + 5x - 1 (a quadratic polynomial).

Quartic equations are just one type of polynomial equation.

What Does "Degree" Mean?

The "degree" of a polynomial equation tells you the highest power of the variable in that equation.

• If the highest power is 1 (like 2x + 5 = 0), it's a first-degree or linear equation.
• If the highest power is 2 (like x² + 3x - 4 = 0), it's a second-degree or quadratic equation.
• If the highest power is 3 (like 2x³ - x + 7 = 0), it's a third-degree or cubic equation.

So, a quartic equation is a fourth-degree equation because its highest power is 4.

How are Quartic Equations Different?

Quartic equations are more complex than the simpler equations you might have learned about, like linear or quadratic ones.

Simpler Equations: Linear and Quadratic

You can solve linear equations quite easily. For example, if 2x + 4 = 10, you can quickly find that x = 3. Quadratic equations are a bit harder, but there's a famous "quadratic formula" that helps you find the answers. This formula always works for any quadratic equation.

The Challenge of Solving Quartic Equations

For a long time, mathematicians tried to find a general formula to solve equations of the third and fourth degree. It was a big challenge! Eventually, they did find formulas for cubic and quartic equations. However, these formulas are much longer and more complicated than the quadratic formula. They often involve many steps and can be quite tricky to use.

History of Quartic Equations

The history of solving quartic equations is quite interesting and involves some famous mathematicians from the 16th century in Italy.

• Around the 1500s, mathematicians like Scipione del Ferro and Niccolò Fontana Tartaglia worked on solving cubic equations.
• Then, a mathematician named Lodovico Ferrari, who was a student of Gerolamo Cardano, found a way to solve quartic equations. He figured out how to turn a quartic equation into a cubic equation, which could then be solved using the methods already discovered.
• Cardano published Ferrari's solution in his famous book, Ars Magna, in 1545. This was a huge step forward in algebra!

See also

• Algebra
• Polynomial
• Equation
• In Spanish: Ecuación de cuarto grado para niños

Images for kids

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  Graph of a polynomial function of degree 4, showing its 4 roots (where it crosses the x-axis) and 3 critical points (where the curve changes direction).

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  The quartic formula, which is used to find the solutions to a quartic equation. It is much more complex than the quadratic formula.