x mathematics conceptuals chapter -2

Degree of the polynomial :-  If p(x) is a polynomial in terms of  x, the highest power of x in p(x) is called the degree of the polynomial p(x).

For example,

 3x + 2 is a polynomial of  x.  Degree of expression is 1

 4z^2 –z + 2 is a polynomial of z.  Degree of expression is 2,

3x^3 – 2x – 2 is a polynomial of x.  Degree of expression is 3

Type of polynomials

linear polynomial :- A polynomial of degree 1 is called a linear polynomial.         

For example, 7x + 43,

quadratic polynomial :-  A polynomial of degree 2 is called a quadratic polynomial.

For example  x^2 + 3x + 7

cubic polynomial :- A polynomial of degree 3 is called a cubic polynomial

For example  x^3 + 3x

Zeros of the polynomial :-  A real number t  is called a zero of a polynomial if the value of f(t) = 0

For example  

f(x)  = x^2 – 6x +8

zeros of this equation are 2 and 4 because

f(2)= 2^2 -6*2 + 8 = 0

f(4)= 4^2 – 6*4 + 8 =0

Sum and product of root of quadratic equation   :-

For a equation ax^2 + bx  + c  = 0 , if  root are α and β ,

Roots for cubic equation :-

For a equation ax^3 + bx^2 + cx + d  = 0

Division Algorithm:- If p(x) and g(x) are any two polynomials with g(x) is not equal to 0, then we can find polynomials q(x) and r(x) such that

If r(x) = 0 or degree of r(x) < degree of g(x).

Dividend         = Divisor × Quotient   + Remainder

p(x)          = g(x)     × q(x)          + r(x),