Introduction of polynomial

-

Polynomial – An expression containing variable and constant, power of variable must be whole number. For example

   3+x2, 4+6x2





Standard representation of polynomial--     

                                    a0+a1x+a2x2+a3x3+-----------anxn        where a0, a1, a2, ……… an are real number and also called coefficient of polynomial and n is whole number.
Checking polynomial----- its true or false
ü  X2+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 a polynomial-- a polynomial p(x)=0 when x=a then p(a)=0 so x=a is a zeroes of a polynomial
for example     x+1=0 
if x= - 1 

 https://youtu.be/lFtkmOuNRns

               

Popular posts from this blog

Special question of sum and product of roots

-
v     v     Q. (1). If 1,2,3 are the roots of the equation x 3 +ax 2 +bx+c=0 then what is the value of c? Ans. Apply product of roots αβγ= -c/a=- constant term/coefficient of x 3                            1x2x3 =   -c/1 →   6 = -c →   c= - 6 Q.2. If (x+√2) is a factor of kx 2 -√2 x + 1, then what is the value of k? Ans. Putting value of x in given equation so    x+ √ 2=0 then x= - √ 2 →   k (- √ 2) 2 - √ 2 × (-√ 2) +1 = 0                                                  2k+2+1=0                                                                   2k+3=0 →   2k=-3   → k = -3/2 Q.3. What is the factor of the equation (x² -5x) ² -30 (x² -5x) -216=0? Ans.  First of all, let x 2 –5x =y then equation become y 2 –30y-216=0 then factorize 216 in two term for example 216=36×6 so, can be written 30y = 36y-6y so y 2 -(36y-6y)-2016=0             y 2 -36y+6y-216=0 taking common we get y(y-36) +6(y-36) =0       so     (y-36) (y-6) =0 then y has two values
Read more

Sum and product of roots/zeroes

-
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
Read more