Degree of an Equation

Degree of an equation and number of roots of equation are same if it does not have any repeated roots. If repeated roots are there in any equation then degree must be greater than number of distinct roots.

If equation is (X-3)(X-1)(X-5)=0

then

 Degree of the equation is=3=Number of roots.The roots are 3,1 and 5.

If an equation is (X-5)³=0. Then

Degree of the equation= 3≠Number of roots. (Here only one root i.e. X=5)

If an equation is (X-2)(X-5)³=0, then 

Degree of the equation =4 ≠ Number of roots.(only two roots i.e. 2 and 5)

If   f(x)= Xᵃᴵᵇ+ Xᶜᴵᵈ + Xᵉᴵᶠ = 0 is any equation where  a/b, c/d, e/f  are fractions in simplest form. Then to determine it's degree multiply numerator and denominator of  a/b, c/d, e/f  such that denominators of all the terms are the same, then highest value of numerator of these terms is degree of equation.

Ex: To find degree of the equation X¹ᴵ²+X¹ᴵ³+X¹ᴵ⁴ = 0.

Fraction powers are 1/2, 1/3, 1/4. Here make denominators of all fractions to be same. Multiply numerator and denominator with 6,4 and 3  respectively. So they become 6/12, 4/12 and 3/12. So degree of given equation is 6.