Competitive Maths

Sum and Product of roots/zeroes of a polynomial-                          Standard quadratic equation of a polynomial is ax 2 +bx+c=0, where a, b,c is constant.    Let α and β are roots of a polynomial then factors are (x- α ) (x- β) = 0                                                                                        x 2 -xβ-xα+αβ=0                                                                                        x 2 -x(α+β) +αβ=0                                                  Compare standard equation of polynomial then         α+β= - b/a = - coefficient of x/coefficient of x 2        αβ = c/a = constant term/coefficient of x 2     Q.1. The roots of the equation x²-2x+3=0 are α and β. What is the equation whose roots are α², β²? Ans. Let α and β are the roots of the equation x²-2x+3=0 then sum and product of the roots α+β= - b/a = - coefficient of x/coefficient of x²=-(-2)/1=2 αβ = c/a = constant term/coefficient of x² =3/1=3 then

Polynomial – An expression containing variable and constant, power of variable must be whole number. For example     3+x 2 , 4+6x 2 Standard representation of polynomial--                                          a 0 +a 1 x+a 2 x 2 +a 3 x 3 +-----------a n x n         where a 0 , a 1 , a 2 , ……… a n are real number and also called coefficient of polynomial and n is whole number. Checking polynomial----- its true or false ü   X 2 +2x+1 ü   X+1/x   √   x+1/2 Degree of polynomial— In polynomial highest power of variable is called degree of polynomial. Based on degree there are mainly three types of polynomial 1 .Linear polynomial — a polynomial having degree is 1 is called linear polynomial and at most one zeroes. 2. Quadratic polynomial —a polynomial having degree is 2 is called quadratic polynomial and at most two zeroes. 3. Cubic polynomial — a polynomial having degree is 3 is called cubic polynomial and at most three zeroes. Zeroes of

2+3=5 1+11=12