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- 1. NAME – Nihas Kamarudheen CLASS- X - C ROLL NO-30 A presentation on
- 2. WHAT IS A POLYNOMIAL
- 3. On the basis of degree
- 4. 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.
- 5. 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
- 6. 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.
- 7. 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