Geometrical Meaning of Zeros of a Polynomial

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

1. None of the above
2. 
3. 
4. 

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. (ii) only

4. (i), (ii) and (iv)

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

Q.

The graph of a quadratic polynomial is a parabola which cuts the X- axis at

1. at most three points

2. four points

3. at most two points

4. one point only

Q.

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

1. A)

2. D)

3. C)

4. B)

Q.

Find the roots of the equation: x-5=0

1. 5

2. -5

3. 0

4. Not defined.

Q.

Question 1
The graphs of y = p(x) are given in the following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Q.

The zero of the polynomial that this graph represents is

1. (2, 0)

2. (0, -2)

3. (-2, 0)

4. (0, 2)

Q.

If the point $(5,0),(0-2)$ and $(3,6)$ lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?

1. $5$

2. Not defined

3. $6$

4. $-2$

Q. When $6$ new boys were admitted and $6$ girls left from the class, the percentage of girls decrased from $68$ to $56$. Find the original number of boys and girls in the class.

1. Number of boys $=14$
   Number of girls$=32$
2. Number of boys $=18$
   Number of girls$=36$
3. Number of boys $=12$
   Number of girls$=30$
4. Number of boys $=16$
   Number of girls$=34$

Q.

Question 2 (vi)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Q.

The graph of the polynomial f(x) = 2x - 5 crosses the X-axis at the point

1. (4, 3)

2. (0, 0)

3. (5/2, 0)

4. (1, -3)

Q.

Sum and the product of zeroes of the polynomial x² +7x +10 is

1. 7/10 and -7/10

2. 7 and -10

3. 10/7 and -10/7

4. -7 and 10

Q.

If the zeroes of the polynomial $P\left(x\right)=a{x}^2+bx+c$ are 1 and 2 , then find the value of a, b and c.

1. a = 1, b = -3 , c = 1

2. a = 3, b = -1, c = 1

3. All of these

4. a = 1 , b = -3, c = 2

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.

The graph of y = p(x) is given. How many zeroes can exist? Assume that the p(x) is always increasing beyond x = 10.

1. 0

2. 2

3. 3

4. 1

Q. If the graph of the polynomial f(x) is as shown in the given figure, then the number of distinct positive zeroes of f(x) is

1. 6
2. 4
3. 5
4. 7

Q.

The graph of y = p(x) is given. How many zeroes can exist?

1. 1

2. 2

3. 3

4. 4

Q.

All polynomials are rational expressions, but all rational expressions need not be a polynomial. State whether the statement is true or false.

1. True

2. False

Q.

Find the polynomial function $f\left(x\right)$ of least degree having only real coefficients and zeros as given.

Assume multiplicity $1$.

$0,-i\text{and}2+i$.

Q.

True or False Questions

Number of zeroes of a polynomial cannot exceed its degree.

1. True
2. False

Q. The point at which a polynomial cuts the x-axis is called the of the polynomial.

1. zero
2. value
3. degree
4. coefficient

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

Q. The graph of a polynomial $y=p\left(x\right)$ is given below. By looking at the graph, find the number of zeroes of $p\left(x\right)$.

Q. Draw the graph of $p\left(x\right)=x^2+3x-4$ and find zeroes.
Verify the zeroes of the polynomials

Q.

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

(i)

(ii)

(iii)

(iv)

(v)

(v)

Q. Construct a graph which represent the zeroes of the quadratic polynomial for an equation$y=x^2-10x$.

Q. Find the number of zeroes of the polynomial from the graph given below.

Q. The graph of a polynomial is as shown in the given figure. The number of real zeroes of the polynomial is

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

Q. The graph of $y=p\left(x\right)$ is given in figure for some polynomial $p\left(x\right)$. The number of zeros of $p\left(x\right)$ are