EXERCISE 2.4 1.Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: (i) 2×2+ x2 – 5x + 2; , 1,-2 (ii) x3 – 4×2 + 5x – 2; 2, 1, 1 Sol. (i) Comparing the given polynomial …
EXERCISE 2.3 1.Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x3-3×2+ 5x – 3, g (x) = x2 _ 2(ii) p(x) =x3 + 3×2+ 4x, g(x) = x2 + 1-x(iii) p(x) = x4– 5x+ 6, g(x) = 2 – x2 Sol. …
EXERCISE 2.2 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients: (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6×2 – 3 – 7x (iv)4u2 +8u (v) t2 – 15 (vi) 3×2 – x – 4 Sol. (i) We have, x2 – 2x – 8 = x2 – 2x …
EXERCISE 2.1 1. The graphs of y = p(x) are given in figures below for some polynomials p(x). Find the number of zeroes of p(x), in each case. Sol. (i) There are no zeroes as the graph does not intersect the x-axis. (ii) The number of zeroes is one as the graph intersects the x-axis …
POLYNOMIALS 1. An algebraic expression p(x) of the form p(x) = a0 , + a1x+a2 x2+ … + anxn, where a0, a1, a2, …, an are real numbers and all the indices of x are non-negative integers, is called a polynomial in x and the highest index n is called the degree of the polynomial, if an 0 …