Class 10 Maths Polynomials Polynomials

Polynomials

 

The deal in the family is that, if Rosy gets x marks in her exam, her brother will give her 2x chocolates, her mother promised to give her x2 chocolates, her dad promised to give her x3 chocolates? How many chocolates will get?

Number of Chocolates Rosy will get, if she scored x marks is p(x) = 2x + x2 + x3

Number of Chocolates Rosy will get, if she scored 1 mark is p(1) = 2*1 + 12 + 13  = 4

Number of Chocolates Rosy will get, if she scored 2 mark is p(2) = 2*2 + 22 + 23  = 16

Number of Chocolates Rosy will get, if she scored 3 mark is p(3) = 2*3 + 32 + 33  = 42

The general expression p(x) = 2x + x2 + x3  is a polynomial.

Use of Polynomial in day to day life: We come across polynomial when we have to find area of a figure with variable dimensions. Also the formula to calculate compound interest on your money deposited in bank is a polynomial. It is also used in Physics, Chemistry & other field of science. Distance travelled by a ball on throw or bullet on fire can be calculated using a polynomial formula, S= ut + ½ at2

What we already know:

  • Polynomials in one variable and their degrees. E.g. p(x)=3x2 +4x + 2
  • If p(x) is a polynomial in x, highest power of x in p(x) is called degree of p(x). g. for polynomial p(x)= 3x2 +4x + 2, highest power is 2, & thus degree is 2.
  • A polynomial of degree 1 is called a linear polynomial. E.g. p(x)=3x +4
  • A polynomial of degree 2 is called a quadratic polynomial E.g. p(x)=3x2 +4
  • A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c, where a, b, are real numbers with a ≠ 0.
  • A polynomial of degree 3 is called a cubic polynomial. E.g. p(x)=3x3 +4
  • If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).g. p(x)=3x +4 , p(2) = 3*2 + 4 = 10.
  • A real number k is said to be a zero of a polynomial p(x), if p(k) = 0. g. p(x) =x3 -27, p(3)=0, thus 3 is said to be Zero of polynomial . p(x)=x3 -27 

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