10th CBSE MATHS FORMULAE CHAPTER NO.2 POLYNOMIALS

CHAPTER NO. 2 POLYNOMIALS

(1) An Algebraic equation :-

General Form:-

P(x)=aₒxⁿ+a_nxⁿ⁻¹+--------------+a_n-1x+a_{n is called polynomial.
Where}   aₒ, aₗ , a,...….,a_n-1,a_{n are constant,}  aₒ ≠ 0.

Degree of polynomial 🠖 n( Highest degree of polynomial) 

   (Ⅰ) Linear Polynomial:-

If n=1 then it is called linear polynomial 

General form:-

ax+b, where a≠ 0.

• Degree 🠆 n= 1
• This equation have atmost 1 roots (zeros)
• Relation between zero`s and coefficient of linear polynomial.                                                         ax+b=0                                                                                                                             x=-b/a 

(Ⅱ) Quadratic polynomial:-

If n=2(degree) then it is called quadratic polynomial 

General form :- ax²+bx+c, where a≠ 0.

• Degree n=2
• Qaudratic polynomial have almost 2 roots (zeros)
• Relation between zeros and coefficient:-                                                                               Let ⍺,𝛽 be zeros of given polynomial ax²+bx+c=0 ⍺+𝛽=-b/a  (Sum of zeros),                                 ⍺.𝛽=c/a  (product of zeros)

(Ⅲ) Cubic polynomial:-

If n=3(degree) then it is called cubic polynomial 

General form:-  ax+bx+cx+d , where a=0

 ⍺+𝛽+𝛾 =-b/a      (Sum of zeros)

 ⍺𝛽+𝛽𝛾+𝛾⍺ =c/a

 ⍺𝛽𝛾 =-d/a           (product of zeros)

(2) Division Algorithm of polynomials:-

If P(x) and g(x) are two polynomial with g(x)≠0 , then find q(x) and r(x) 

such that, 

Divident = Divisor x Quotient + Remainder

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

(3) If are zeros of ax+bx+c=0 then,

1. 1/⍺ + 1/𝛽 =  ⍺+𝛽/⍺.𝛽
2. ⍺²+𝛽² =  (⍺+𝛽)-2⍺.𝛽
3. ⍺³+𝛽³ =  (⍺+𝛽)³-3⍺.𝛽(⍺+𝛽)

   4.  ⍺⁴+𝛽⁴ = (⍺²+𝛽²)²-2(⍺.𝛽)²                                                                                                                 = ((⍺+𝛽)²-2(⍺.𝛽)²-2(⍺.𝛽)²                                                                                                  = (⍺+𝛽)⁴-4(⍺.𝛽)(⍺+𝛽)²+2(⍺.𝛽)²