# Polynomials CLASS 10

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20-Nov-2014Category

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### Transcript of Polynomials CLASS 10

- 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 is a zero of a polynomial f(x), if f() = 0. e.g. f(x) = x - 6x +11x -6 f(2) = 2 -6 X 2 +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 , and be the zeroes of the polynomial ax + bx + cx Then, sum of zeroes(++) = -b = -(coefficient of x) a coefficient of x + + = c = coefficient of x a coefficient of x Product of zeroes () = -d = -(constant term) a coefficient of x 6. QUESTIONS BASED ON POLYNOMIALS I) Find the zeroes of the polynomial x + 7x + 12and verify the relation between the zeroes and its coefficients. f(x) = x + 7x + 12 = x + 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 = -4 and = -3. 7. 2) Find a quadratic polynomial whose zeroes are 4, 1. sum of zeroes, + = 4 +1 = 5 = -b/a product of zeroes, = 4 x 1 = 4 = c/a therefore, a = 1, b = -4, c =1 as, polynomial = ax + bx +c = 1(x) + { -4(x)} + 1 = x - 4x + 1 THE

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