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Polynomials Test - 13

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Polynomials Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following expressions is a polynomial with one variable?

A
x²+ y

B
y – x

C

D
– x² – 2

Solution

-x² – 2 is the only option that contains one variable.
Question 2
1 / -0

Which of the following numbers represents the sum of zeros of the polynomial x² – 9?

A
–6

B
6

C
0

D
9

Solution

The given equation is x² – 9
Sum of zeros = ^.comparing the the equation x² - 9 with ax² + bx + c
we get a = 1, b = 0
so, In x² – 9 sum of zeros = = 0
Question 3
1 / -0

Which of the following ordered pairs represents the point of intersection of y = x² – 2x + 1 and the x-axis?

A
(– 1, 0)

B
(1, 0)

C
(0, 1)

D
(2, 0)

Solution

y = x² – 2x + 1 ….. (1)
At x-axis, y = 0 ….. (2)
Solving (1) and (2), we get
x² + 1² – 2 (x) (1) = 0
Using a² + b² – 2ab = (a – b)²(x – 1)² = 0
x – 1 = 0 x = 1
So, point of intersection = (1, 0)
Question 4
1 / -0

Which of the following expressions does not have a defined zero?

A
x + 1

B
x² + 1

C
x +

D
x² – 2

Solution

x² + 1
Put the above expression equal to 0 to find the zeroes.
x²+ 1 = 0 x² = – 1
x =, which is not defined.
Question 5
1 / -0

Which of the following numbers represents the sum of zeros of the polynomial x²– () x + ?

A

B

C

D

Solution

x² – x – x +.
x (x – ) – (x – )
(x –) (x –)
So, the zeros are and .
Sum of zeros = +
Alternatively:
x² –
Sum of roots =
Question 6
1 / -0

If x = -1, what is the value of P(x) = 5x² + 2x – 3?

A
4

B
6

C
0

D
10

Solution

P(x) = 5x² + 2x – 3
At x = –1,
P(-1) = 5(-1)² + 2(-1) – 3
P(-1) = 5 – 2 – 3 = 0
Question 7
1 / -0

Which of the following polynomials has the product of zeroes equal to ?

A
x² + 8x + 7

B
x²+ 7x + 8

C
7x²+ 8x + 1

D
7x² + x + 8

Solution

In the expression ax² + bx + c, product of roots = .
In the expression 7x² + 8x + 1, product of zeroes = .
Question 8
1 / -0

Which of the following pairs represents the zeroes of the polynomial x² + 2x – 15?

A
– 3, – 5

B
– 3, 5

C
3, 5

D
3, – 5

Solution

x² + 2x – 15
On splitting the middle term, we get
x² + (5 – 3) x – 15 [By using x² + (a + b) x + ab = (x + a) (x + b)]
(x + 5) (x – 3)
Zeroes are 3 and – 5.
Question 9
1 / -0

Which of the following ordered pairs represents the point of intersection of y = 2x + 7 and the x–axis?

A
(0, 7)

B
(– 7, 0)

C
(, 0)

D

Solution

y = 2x + 7
At x – axis, y = 0
So put this value of y in the equation = 2x + 7, we get
0 = 2x + 7
x =
Point
Question 10
1 / -0

Which of the following polynomials has the sum of its zeros as '1' and the product of its zeros as '-2'?

A
x² + x – 2

B
x²+ x + 2

C
x²– x – 2

D
x² + 2x + 1

Solution

ax² + bx + c
Product of zeros =
Sum of zeros =
x² – x – 2
Sum = = 1, Product = = –2
x² - (sum of the zeros)x + product of the zeros = 0
x² - x - 2 = 0
Question 11
1 / -0

Which of the following polynomials is a quadratic polynomial?

A
x + 1

B
x³ + x² + x + 1

C
x²

D
x³ + 1

Solution

A quadratic polynomial is the one which has '2' as the maximum power in the polynomial expression.
Hence, the answer is x².
Question 12
1 / -0

Which of the following numbers represents the sum of zeroes of the polynomial x² – 4x + 3?

A
4

B
– 4

C
3

D
– 3

Solution

For the expression ax² + bx + c, sum of zeroes =.
Therefore, sum of zeroes of x² – 4x + 3 = = 4
Question 13
1 / -0

Which of the following polynomials has the sum of zeroes as and the product of zeroes as – 1?

A
2x² – 3x + 2

B
2x² + 3x – 2

C
2x² – 3x – 2

D
2x² + 3x + 2

Solution

For polynomial ax² + bx + c,
Sum of zeroes = and product =
For 2x² + 3x – 2
Sum=and product =
Hence, the polynomial having sum = and product = – 1 is 2x² + 3x – 2.
Question 14
1 / -0

Which of the following ordered pairs represents the point of intersection of y = x and the x-axis?

A
(1, 1)

B
(2, 0)

C
(0, 0)

D
(– 1, 0)

Solution

y = x
At x-axis, y = 0
On solving, we get x = 0.
Point is (0, 0)
Question 15
1 / -0

What is zero of the polynomial 2x²?

A
2

B
0

C
1

D
4

Solution

To find the zero, put 2x² = 0
2x² = 0
x2 = 0
x = 0
Question 16
1 / -0

Which of the following polynomials has the sum of zeroes as and the product of zeroes as ?

A
3x² + x + 10

B
3x² – x + 10

C
3x² + x – 10

D
3x² – x – 10

Solution

For polynomial ax² + bx + c,
Sum of zeroes =and product =.
For 3x² – x – 10,
Sum = = and product =.
Polynomial having sum of zeroes = and product of zeroes as is 3x² – x – 10.
Question 17
1 / -0

The graph of y = p(x) for some polynomial p(x) is given below:

How many zeros of p(x) are there?

A
9

B
10

C
8

D
11

Solution

The number of zeros of the given curve is calculated by counting the number of points where it meets the x-axis.
The given curve has 10 points on the x-axis.
Question 18
1 / -0

Which of the following values is a zero of the polynomial 3x² – 27?

A
– 9

B
3

C
3

D
9

Solution

3x²– 27
Put 3x² – 27 = 0
3x² = 27
x²= 9 and x = 3
3 is the answer.
Question 19
1 / -0

Which of the following expressions is not a polynomial?

A
x² + 2

B
2

C
2x –

D
x

Solution

In polynomials, the variables do not have a negative power.
2x – is not a polynomial.
Question 20
1 / -0

Which of the following values is a zero of the polynomial 2x² – 2?

A
1

B
0

C
2

D

Solution

2x² – 2 = 0
2x² = 2
x²= 1
x = 1
1 is the zero of 2x² – 2.
Question 21
1 / -0

The graph of y = p(x) for some polynomial p(x) is given below.

What is the number of zeroes of p(x)?

A
0

B
2

C
1

D
4

Solution

The number of zeroes for the curve is the point where the curve intersects the x-axis.
Question 22
1 / -0

Which of the following expressions is a polynomial?

A
x² –

B
x⁴

C
x²

D
x² + x^–1

Solution

Since the given curve does not intersect any point on the x-axis, so it has zero number of zeroes.
x⁴= x⁷ – x does not have any power less than 0, so it is a polynomial.
Question 23
1 / -0

Which of the following numbers represents the product of zeroes of the polynomial x² – 3x – 4?

A
4

B
– 4

C

D

Solution

Product of zeroes = for ax² + bx + c
For x² – 3x – 4,
product of zeroes = = – 4
Question 24
1 / -0

Which of the following expressions is a trinomial?

A
1x + 2x^-1+ 3

B
3x + 2

C
x³+ 3x – 2

D
x^1/3

Solution

A polynomial having three terms is called a trinomial.

x³ + 3x – 2 is the required answer.
Question 25
1 / -0

Which of the following polynomials has the sum of zeros as and the product of zeroes as ?

A
2x² – 11x + 5

B
2x² + 11x – 5

C
2x² – 11x – 5

D
2x² + 11x + 5

Solution

For ax² + bx + c = 0,
Sum of zeros = and product of zeros =
For 2x² – 11x + 5,
Sum = and product =
Question 26
1 / -0

Which of the following expressions is not a polynomial with one variable?

A
(

B
(x + 2)²

C
(x + 2) y

D
x – 3

Solution

A polynomial with one variable is the one whose value is dependent on only 1 variable. Out of given options, only (x + 2) y has two variables.
Question 27
1 / -0

The graph of y = p(x) for some polynomial p(x) is given below:

How many zeroes of p(x) are there?

A
1

B
0

C
2

D
5

Solution

For the given curve, the number of zeroes is the number of points where the curve intersects the x-axis.
y = p(x) meets the x-axis only at 1 point.
Number of zeroes = 1
Question 28
1 / -0

Which of the following expressions is a polynomial?

A
(

B
(x + 2)^3/2

C
[(x + 2)²]^3/2

D
+ 2

Solution

= (x + 2)³
= x³ + 6x² + 12x + 8 is a polynomial because the variable has whole number exponent.
Question 29
1 / -0

Which of the following polynomials is a linear polynomial?

A
0

B
1

C
x

D
x²

Solution

Let y be the function i.e. y = x
i.e. as graph of y = x is a st. line as shown in the graph. Hence, x is a linear equation.
Question 30
1 / -0

The graph of y = p(x) for some polynomial p(x) is given below.

What is the number of zeroes of p(x)?

A
2

B
3

C
1

D
4

Solution

For the curve, number of zeroes is number of points where the curve meets the x-axis.
y = p(x) meets x-axis at 1 point.
Number of zeroes = 1
Question 31
1 / -0

Which of the following expressions is a zero polynomial?

A
0

B
3

C

D
x^o

Solution

'0' is a zero polynomial.
Question 32
1 / -0

Which of the following values is a zero of the polynomial x² + 3x + 2?

A
- 1

B
2

C
1

D
0

Solution

x² + 3x + 2
Splitting the middle term, we get
x² + (2 + 1) x + 2
Using x² + (a + b) x + ab = (x + a) (x + b),
x² + (2 + 1) x + 2 = (x + 1) (x + 2)
Put these factors equal to 0 to find the zeroes.
x = – 1 and x = – 2
Question 33
1 / -0

Which of the following numbers represents the product of zeroes of the polynomial 6x² – x – 1?

A

B
6

C
– 6

D

Solution

Product of zeroes =
Question 34
1 / -0

Which of the following expressions is a constant polynomial?

A
2

B
x

C
x + 2

D

Solution

We can write 2 = 2 1 = 2 x°
Therefore, 2 is a constant polynomial as power of variable x is zero.
Question 35
1 / -0

Which of following polynomials has 5 as a zero?

A
x² – 3x – 10

B
2x² + 5x – 25

C
x² + 2x – 15

D
x² + x – 20

Solution

x² – 3x – 10
Splitting the middle term, we get
x² + (– 5 + 2) x + (– 5) (2)
By using x² + (a + b) x + ab = (x + a) (x + b), we get
(x – 5) (x + 2)
Now, x – 5 = 0
x = 5
and x + 2 = 0
x = – 2
x² – 3x – 10 is the required answer.
Question 36
1 / -0

Which of the following ordered pairs represents the point of intersection of y = x + 4 and the x-axis?

A
(– 4, 0)

B
(4, 0)

C
(0, - 4)

D
(0, 0)

Solution

y = x + 4
At x-axis, y = 0
On solving, we get
0 = x + 4
x = – 4
So, (– 4, 0) is the answer
Question 37
1 / -0

Three curves are plotted on the given graph.

Which of the given curves has/have the greatest number of real and distinct zeroes?

A
u

B
v

C
w

D
Both (1) and (3)

Solution

Since the curve u intersects the x-axis at two points, it has the greatest number of real and distinct zeroes.
Question 38
1 / -0

What will be the positive zero of the polynomial x² + 3x – 10?

A
3

B
2

C
5

D
10

Solution

x² + 3x – 10 = 0
x² + 5x – 2x – 10 = 0
x (x + 5) – 2 (x + 5) = 0
(x – 2) (x + 5) = 0
x = 2 and – 5
x = 2 is the answer.
Question 39
1 / -0

Which of the following ordered pairs represents the point of intersection of y = 2x + 1 and the x–axis?

A
(0, 1)

B
(– 1, 0)

C

D

Solution

y = 2x + 1
At x–axis, y = 0.
On solving, we get
0 = 2x + 1
x =
Therefore, is a point of intersection.
Question 40
1 / -0

What is common zero for equations 2x² + x – 10 and x² + 3x – 10?

A
10

B
2

C
- 10

D
0

Solution

2x² + x – 10 = 0
2x² + 5x – 4x – 10 = 0,
x(2x + 5) – 2 (2x + 5) = 0,
(x – 2) (2x + 5) = 0,
x = 2,
x² + 3x – 10 = 0
x² + 5x – 2x – 10 = 0
x(x + 5) – 2 (x + 5) = 0
(x – 2) (x + 5) = 0
x = 2, – 5
Common zero = 2

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