Question

What are higher-order equations in the quadratic equations?

Answer 1

Determine the higher-order equations in the quadratic equations.

Higher-Order equations are described as equations of the type $f\left(x\right)=0$ with a degree larger than$3$. A degree of $f\left(x\right)$ is equal to the number of roots of an equation with real coefficients.

The higher-order equation can be solved by factorization, the factor theorem, or by reducing it to one of the lower-order equations. The factor theorem is defined as $(x-a)$a factor of $f\left(x\right)$ if $f\left(a\right)=0$.

fifth-degree equation: $a{x}^5+b{x}^4+c{x}^3+d{x}^2+e=0$

• root sum$=-\frac{b}{a}$
• Sum of pairwise products of roots$=\frac{c}{a}$
• Root product sums taken three at a time $=-\frac{d}{a}$
• Root product sums taken four at a time $=\frac{e}{a}$
• root product $=-\frac{f}{a}$

Hence, the Higher-Order equations are described as equations of the type $f\left(x\right)=0$ with a degree larger than$3$.