Class 10 Chapter 2(Poloynomials)
Case based 2:
While passing over an iron bridge, Hema noticed that the shape resembles a curve about which she had studied in mathematics.(Class 10 Case based problem of Chapter 2 Polynomials 2)
(A) What type of ploynomial does the shape of the bridge represents ?
(B) Find the zeroes of the polynomial x² + 7x – 60
Solution: (A) The shape of the bridge represents quadratic polynomial
(B) To find the zeros of the polynomial x² + 7x – 60, we need to factorize the polynomial.
x² + 7x – 60 = x² + 12x – 5x – 60
= x(x + 12) -5(x + 12)
= (x + 12)(x – 5)
Therefore zeros of the polynomial = 5 , -12
Case based 3:
Due to heavy storm, an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following question below:
(A) Name the shape in which the wire is bent.
(a) Spiral (b) Ellipse
(c) Linear (d) Parabola
(B) How many zeros are there for the polynomaial(shape of the wire)
(a) 2 (b) 3
(c) 1 (d) 0
(C) The zeros of the polynomial are
(a) -1, 5 (b) -1, 3
(c) 3, 5 (d) -4, 2
(D) What will be the expression of the polynomial?
(a) x² + 2x – 3 (b) x² – 2x + 3
(c) x² – 2x – 3 (d) x² + 2x + 3
(E) What is the value of the polynomial if x = -1?
(a) 6 (b) -18
(c) 18 (d) 0
(A) Answer (d) Parabola
(B) Answer (a) 2
Graph of the polynomial intersect x-axis at two points
Hence, number of zeroes of the polynomial = 2
(C) Answer (b) -1, 3
We know, points at which graph of a polynomial intersect the x- axis,are the zeros of the polynomial. Here, The graph intersects x-axis at points -1 and 3
Its zeros are = -1 and 3
(D) Answer (c) x² – 2x – 3
We have the zeros of the polynomial are -1 and 3
Then quadratic equation is
= x² – (Sum of zeroes) x + Product of zeroes
= x² – (-1 + 3)x + (-1)(3)
= x² – 2x – 3