Polynomials Test

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Polynomials Test - 1

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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
√xy

D
– x² – 2

Solution

-x² – 2 is the only option that contains one variable.
Question 2
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 3
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 4
1 / -0

Which of the following polynomials has the product of zeroes equal to 1/7?

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 = c/a.
In the expression 7x² + 8x + 1, product of zeroes = 1/7.
Question 5
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.

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Re-Attempt Weekly Quiz Competition

Polynomials Test - 1

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Polynomials Test - 1

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SHARING IS CARING

Question 1

x2 + y

y – x

√xy

– x2 – 2

Solution

Question 2

(– 1, 0)

(1, 0)

(0, 1)

(2, 0)

Solution

Question 3

4

6

0

10

Solution

Question 4

x2 + 8x + 7

x2 + 7x + 8

7x2 + 8x + 1

7x2 + x + 8

Solution

Question 5

– 3, – 5

– 3, 5

3, 5

3, – 5

Solution

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x²+ y

– x² – 2

x² + 8x + 7

x²+ 7x + 8

7x²+ 8x + 1

7x² + x + 8