Geometrical Meaning of Zeros of Polynomial

Q.

How to find zeros of cubic polynomial?

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 question.

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

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

Q. by watching a graph of polynomial , how can be find the value of a , b , c that they are less than 0 or greater than 0

Q. Three curves i.e.
a) $y=x^2$
b) $y=x^4$
c) $y=x^6$
are depicted in the graph shown below. Which of the polynomials does the graph 3 represent?

1. $y=x^2$
2. $y=x^4$
3. $y=x^6$
4. cannot be determined

Q. 6. A cubic polynomial fx)axbx2 + cx + d hasa graph which touches the x-axis at 2, has anox-intercept at-1 and has y-intercept at -2 as shown. Thevalue of, a +b+c+ d equals to431/2 3 42

Q. Choose the correct statement(s).

i) A linear polynomial has only one zero.
ii ) A quadratic polynomial will have two zeroes.
iii) A quadratic polynomial can have a maximum of two zeroes.
iv) A cubic polynomial can have a maximum of three zeroes.

1. (ii) only
2. (i), (iii) and (iv)
3. (i), (ii) and (iv)
4. (ii) only

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

Q.

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

1. 

2. 

3. 

4. 

Q. Identify the number of zeroes of the polynomial represented by the graph shown below.

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

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 graph represents a quadratic polynomial which has sum of its zeroes is zero?

1. A)

2. B)

3. C)

4. D)

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

Q. If a polynomial p(x) is of degree “n”, the graph of the polynomial should cut the X axis at “n” points.

1. True
2. False