Polynomials CLASS 10
This document contains a presentation on polynomials. It defines what a polynomial is and discusses how the degree of a polynomial relates to the number of zeros. It provides an example of a cubic polynomial and discusses the relationship between the zeros and coefficients of a cubic polynomial. Specifically, it states that the sum of the zeros equals the negative of the coefficient of x^2, the sum of the products of the zeros equals the coefficient of x, and the product of the zeros equals the negative of the constant term. The document then provides two example questions - one asking to find the zeros of a quadratic polynomial and verify the relationship between the zeros and coefficients, and another asking to find a quadratic polynomial with given zeros.
![QUESTIONS BASED ON
POLYNOMIALS
I) Find the zeroes of the polynomial x² + 7x + 12and verify the relation between the
zeroes and its coefficients.
f(x) = x² + 7x + 12
= x² + 4x + 3x + 12
=x(x +4) + 3(x + 4)
=(x + 4)(x + 3)
Therefore,zeroes of f(x) =x + 4 = 0, x +3 = 0 [ f(x) = 0]
x = -4, x = -3
Hence zeroes of f(x) are α = -4 and β = -3.](https://image.slidesharecdn.com/polynomials-120726050407-phpapp01-140706095435-phpapp02/85/Polynomials-CLASS-10-8-320.jpg)
More Related Content
What's hot (20)
Viewers also liked (20)
Similar to Polynomials CLASS 10 (20)
Recently uploaded (20)
Polynomials CLASS 10
- 1. NAME – Nihas Kamarudheen CLASS- X - C ROLL NO-30 A presentation on
- 2. WHAT IS A POLYNOMIAL
- 4. On the basis of degree
- 5. A real number α is a zero of a polynomial f(x), if f(α) = 0. e.g. f(x) = x³ - 6x² +11x -6 f(2) = 2³ -6 X 2² +11 X 2 – 6 = 0 . Hence 2 is a zero of f(x). The number of zeroes of the polynomial is the degree of the polynomial. Therefore a quadratic polynomial has 2 zeroes and cubic 3 zeroes.
- 7. Relationship between the zeroes and coefficients of a cubic polynomial • Let α, β and γ be the zeroes of the polynomial ax³ + bx² + cx • Then, sum of zeroes(α+β+γ) = -b = -(coefficient of x²) a coefficient of x³ αβ + βγ + αγ = c = coefficient of x a coefficient of x³ Product of zeroes (αβγ) = -d = -(constant term) a coefficient of x³
- 8. QUESTIONS BASED ON POLYNOMIALS I) Find the zeroes of the polynomial x² + 7x + 12and verify the relation between the zeroes and its coefficients. f(x) = x² + 7x + 12 = x² + 4x + 3x + 12 =x(x +4) + 3(x + 4) =(x + 4)(x + 3) Therefore,zeroes of f(x) =x + 4 = 0, x +3 = 0 [ f(x) = 0] x = -4, x = -3 Hence zeroes of f(x) are α = -4 and β = -3.
- 10. 2) Find a quadratic polynomial whose zeroes are 4, 1. sum of zeroes,α + β = 4 +1 = 5 = -b/a product of zeroes, αβ = 4 x 1 = 4 = c/a therefore, a = 1, b = -4, c =1 as, polynomial = ax² + bx +c = 1(x)² + { -4(x)} + 1 = x² - 4x + 1 THE