Worksheet for chapter: Polynomials is presented below. The worksheets are provided for practice and self evaluation of students of class 10. Solutions are provided at the end of the page.
(1) The graphs of y = p(x) are given in figure given below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
(2) Find a quadratic polynomial, the sum and product of whose zeroes are -5 and -10 respectively.
(3) Divide x2 + 2x + 4 by polynomial x+1 and find quotient and remainder.
(4) Find the zeroes of polynomial x2 + 10x – 25. Verify relationship between zeroes and the coefficients.
(5) Find the zeroes of polynomial 2 x2 -5x + 2.
(6) On dividing x3 – 2x2 + 2x + 2 by a polynomial g(x), the quotient and remainder were x- 4 and 2x + 6 respectively.
(7) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
x -2, x3 + 2x2 – 4x + 8
(8) Find all other zeroes of the of x3 + x2 + 2x + 2 , if one zero is -1.
(9) Divide x2 + 10 x + 16 by x + 3
(10) State whether statement is ‘True’ or ‘False’.
(i) A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
(ii) If are the zeroes of te cubic polynomial ax3 + bx2 + cx + d, then
α + β + γ = c/a
(iii) If p(x) and g(x) are any to polynomials with g(x) 0, then we can find polynomials q(x) and r(x) such that
p(x) = g(x) r(x) + q(x),
where r(x) = 0 or degree of r(x) < degree of g(x).