Geometrical Meaning of Zeros of Polynomial

Q.

Which of the following graph represents the quadratic polynomial $-x^2+5x-6$?

1. 

2. 

3. 

4. 

Q. A polynomial $y=f\left(x\right)$ when represented on graph cuts $x-\text{axis}$ at 2 points and $y-\text{axis}$ at 3 points. What is the number of zeroes of $f\left(x\right)$ ?

1. \N
2. 3
3. 5
4. 2

Q. The number of times the graph of y = p(x) cuts the X axis is ‘a’. The degree of the polynomial p(x) is ‘b’ (> 0). Then $\frac{b}{a}$ ___ 1

1. <
2. >
3. $\ge$
4. $\le$

Q. What is the maximum number of times the graph of the polynomial $y=p{x}^3+q{x}^2+rx+s$ intersects the x axis?

1. 1
2. 2
3. 4
4. 3

Q.

Polynomials in Real Life

Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.

Based on the given information, answer the following question:

If the path traced by the Roller Coaster is represented by the above graph $y=p\left(x\right)$ , find its zeroes?

1. -1, 1, 4

2. -2, -1, 2
   
3. -1, 1, 2
4. -2, 1, 4

Q. The graph of y = p(x) is given. Assuming p(x) increases from x=10, the number of zeroes of y = p(x) is ___.

Q. A polynomial $y=f\left(x\right)$ when represented on graph cuts $x-\text{axis}$ at 2 points and $y-\text{axis}$ at 3 points. What is the number of zeroes of $f\left(x\right)$ ?

1. \N
2. 3
3. 5
4. 2

Q. Plot the graph of 0 (ZERO) Polynomial by constructing a equation and explaining it.

Q.

Polynomials in Real Life

Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.

Based on the given information, answer the following question:

If the path traced by the Roller Coaster is represented by the above graph $y=p\left(x\right)$ , find its zeroes?

1. -1, 1, 4

2. -2, -1, 2
   
3. -1, 1, 2
4. -2, 1, 4

Q. What will be the sign of constant of the quadratic polynomial if the parabola of the graph of the polynomial doesnt cut the Y-axis?

Q. What is the maximum number of times the graph of the polynomial $y=p{x}^3+q{x}^2+rx+s$ intersects the x axis?

1. 1
2. 2
3. 4
4. 3

Q. Three curves i.e. $a)y=3x^2,b)y=5x^2\&c)y=7x^2$ are depicted in the following graph. Identify correct relation.

1. (a)-(1) , (b)-(2), (c)-(3)
2. (a)-(3) , (b)-(2), (c)-(1)
3. (a)-(2) , (b)-(1), (c)-(3)
4. (a)-(2) , (b)-(3), (c)-(1)

Q. What is the maximum number of times the graph of the polynomial $y=p{x}^3+q{x}^2+rx+s$ intersects the x axis?

1. 1
2. 2
3. 4
4. 3

Q. What is the maximum number of times the graph of the polynomial $y=p{x}^3+q{x}^2+rx+s$ intersects the x axis?

$\left[2\right]$

Q. A polynomial $y=f\left(x\right)$ when represented on graph cuts $x-\text{axis}$ at 2 points and $y-\text{axis}$ at 3 points. Find the number of zeroes of $f\left(x\right)$ .

Q. The graph of y = p(x) is given. The number of zeroes of y = p(x)​ is___.

1. 0
2. 1
3. 2
4. 3

Q. The graph of a linear polynomial is a straight line.

1. True
2. False

Q. The number of times the graph of y = p(x) cuts the X axis is ‘a’. The degree of the polynomial p(x) is ‘b’ (> 0). Then $\frac{b}{a}$ ___ 1

1. >
2. <
3. $\ge$
4. $\le$

Q. Which of the following graphs represent the polynomial $y=p\left(x\right)$ which has only two zero?

Q.
Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range.

Based on the given information, answer the following questions.

(i) If the equation of the bridge is represented by the following graph $y=p\left(x\right)$, then name the type of the polynomial it traces.


(A) Linear
(B) Quadratic
(C) Cubic
(D) Bi-quadratic

(ii) If the path traced by the hills is represented by the graph $y=p\left(x\right)$ below, find the number of zeroes.


(A) 0
(B) 1
(C) 2
(D) 3​​​

(iii) Find a quadratic polynomial for the bridge if 6 is the sum and 8 is the product of its zeroes.

(A) $x^2+6x+8$
(B) $x^2-6x+8$
(C) $x^2+6x-8$
(D)​​​ $x^2-6x-8$

Q. what is the sign of c if the parobola or the graph of the polynomial does not cut the y axis

Q. What is the maximum number of times the graph of the polynomial $y=p{x}^3+q{x}^2+rx+s$ intersects the x axis?

1. 1
2. 2
3. 4
4. 3