Class 10 Case based problem of Chapter 2 Polynomials 2
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
=Â x(x + 12) -5(x + 12)
=Â (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) 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 3
(c) 1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 0
(C) The zeros of the polynomial are
(a) -1, 5Â Â Â Â Â Â Â Â Â Â Â (b) -1, 3
(c) 3, 5Â Â Â Â Â Â Â Â Â Â Â Â (d)Â -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) 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) -18
(c) 18Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 0
Solution:
(A) Answer (d) Parabola
(B) Answer (a) 2
Explanation:
Graph of the polynomial intersect x-axis at two points
Hence, number of zeroes of the polynomial = 2
(C) Answer (b) -1, 3
Explanation:
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
Explanation:
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