Question

In a game to entertain themselves, students of class -10th have drawn following figure with chalk on ground. They have some questions in their mind which they want to solve. Please answer and solve their question.
(a) The number of zeroes of the polynomial p(x) is
i) 1 ii) 2 iii) 3 iv) 4
(b) The zeroes of the polynomial are
i) 1,3 ii) -1,3 iii) 1,-3 iv) -1,-3
(c) The expression of the polynomial is
i) x2+4x+3 ii) x2-4x+3 iii) x2+4x-3 iv) x2-4x-3
(d) The value of the polynomial if x= 3 is
i) 24 ii) 0 iii) 18 iv) -6
(e) What is the degree of the polynomial?
i) 0 ii) 1 iii) 2 iv) 3

Answer 1

Answer:

I) 2

ii) 1,3

iii) x²-4x+3

Iv) 0

v) 2

Answer 2

The question is incomplete. Please find the full content below.

Concept:

The zero of the polynomial represented in the graph by the points in which ordinate value i.e. the value of y=0.

Given:

The graph of a polynomial y = p(x) which passes through points (0,1), (1,0), (3,0).

A bunch of questions related to the graph.

Find:

The suitable choices for the given questions.

Solution:

The zeros of the polynomial y = p(x) are given by x = 1,3 (from the given graph), since at x = 1,3 the polynomial gives y = p(x) = 0.

Thus the number of zeros is 2.

(a) The number of zeros of the polynomial p(x) is (ii) 2.

(b) The zeros of the polynomial are (i) 1,3

(c) The choices for the expression are $x^2+4x+3,x^2-4x+3,x^2+4x-3,x^2-4x-3$

Checking the points for the expression we get,

For (1,0):

$x^2+4x+3=1^2+4\times1+3=1+4+3=8\ne0$

$x^2-4x+3=1^2-4\times1+3=1-4+3=0$

$x^2+4x-3=1^2+4\times1-3=1+4-3=2\ne0$

$x^2-4x-3=1^2-4\times1-3=1-4-3=-6\ne0$

Thus the second option is satisfied by the point on the graph.

Hence the correct expression is (ii)

(d) The value of the polynomial if x=3 is given by,

$x^2-4x+3=3^2-4\times3+3=9-12+3=0$

The value is 0, option (ii)

(e) The degree of the polynomial is (iii) 2 since it is a quadratic equation of x.

Hence,

(a) The number of zeros of the polynomial p(x) is (ii) 2.

(b) The zeroes of the polynomial are (i) 1,3.

(c) The expression of the polynomial is (ii) $\mathbf{x^2-4x+3}$.

(d) The value of the polynomial if x= 3 is (ii) 0

(e) The degree of the polynomial is (iii) 2.

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