# Geometrical Meaning of Zeros of a Polynomial

## Trending Questions

**Q.**Which of the following graph represents the quadratic polynomial −x2+5x−6?

- None of the above

**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.

(ii) only

(i), (iii) and (iv)

(ii) only

(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

at most three points

four points

at most two points

one point only

**Q.**

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

A)

D)

C)

B)

**Q.**

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

5

-5

0

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

(2, 0)

(0, -2)

(-2, 0)

(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?

5

Not defined

6

−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.

- Number of boys =14

Number of girls=32 - Number of boys =18

Number of girls=36 - Number of boys =12

Number of girls=30 - 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 x2 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

(4, 3)

(0, 0)

(5/2, 0)

(1, -3)

**Q.**

Sum and the product of zeroes of the polynomial x^{2} +7x +10 is

7/10 and -7/10

7 and -10

10/7 and -10/7

-7 and 10

**Q.**

If the zeroes of the polynomial P(x)=ax2+bx+c are 1 and 2 , then find the value of a, b and c.

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

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

All of these

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.

- (ii) only
- (i), (iii) and (iv)
- (i), (ii) and (iv)
- (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.

0

2

3

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

- 6
- 4
- 5
- 7

**Q.**

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

1

2

3

4

**Q.**

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

True

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.

- True
- False

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

- zero
- value
- degree
- 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(x) is given below. By looking at the graph, find the number of zeroes of p(x).

**Q.**Draw the graph of p(x)=x2+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 equationy=x2−10x.

**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

- 0
- 1
- 2
- 4

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