Relation between the roots of the equation of the Nth degree

Dear Aspirants,

Today we will see what is the relation between the roots of an equation of the N^th degree.

Let the equation of the n^th degree be :

a₀xⁿ + a₁x^n-1 + a₂x^n-2 + …… + a_n , where a₀, a₁, a₂, … a_n are not equal to 0.

Sum of the roots =  (-a₁/a₀)

Sum of the products of the roots taken two at a time=  (a₂/a₀)

Sum of the products of the roots taken three at  a time = (-a₃/a₀)

.

.

.

.

.

Product of the roots =  (-1)ⁿ[a_n/a₀]

Example: Find the relation between the different roots of the equation: (2x⁴ + 10x³ – 8x² +9)

Solution: As the equation is of degree 4, so the number of roots of the equation are 4. Let the roots be : A, B, C and D.

Sum of the roots, (A+B+C+D) = (-10/2) = -5

Sum of products of roots taken two at a time, (AB + BC + CD+ AC + AD + BD )= (-8/4) = -2

Sum of the products of the roots taken three at a time = 0 (As the coefficient of x is 0)

Products of the roots = (AxBxCxD) = 9/2

Thanks!