WBBSE Class 9 Maths Algebra Chapter 4 Polynomial Multiple Choice Questions

WBBSE Class 9 Maths  Algebra Chapter 4 Polynomial Multiple Choice Questions

Example 1. Which of the following is a polynomial is one variable?

1. x + \(\frac{2}{x}\) + 3
2. 3√x + \(\frac{2}{\sqrt{x}}\) + 5
3. √2x² – √3x + 6
4. x¹⁰ + y⁵ + 8

Solution: The correct answer is 3. √2x² – √3x + 6

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Example 2. Which of the following is a polynomial?

1. x – 1
2. \(\frac{x-1}{x+1}\)
3. \(x^2-\frac{2}{x^2}+5\)
4. \(x^2+\frac{2 x^{\frac{3}{2}}}{\sqrt{x^2}}+6\)

Solution: The correct answer is 1. x – 1

Example 3. Which of the following is a linear polynomial?

1. x + x²
2. x + 1
3. 5x² – x + 3
4. x + \(\frac{1}{x}\)

Solution: The correct answer is 2. x + 1

⇒ (For linear polynomial degree will be 1).

Example 4. Which of the followings is a 2nd degree polynomial?

1. √x – 4
2. x³ + x
3. x³ + 2x + 6
4. x² + 5x + 6

Solution: The correct answer is 4. x² + 5x + 6

Example 5. The degree of the polynomial √3 is

1. \(\frac{1}{2}\)
2. 2
3. 1
4. 0

Solution: The correct answer is 4. 0

(√3 = √3 x x°)

The degree of the polynomial √3 is 0

Example 6. If the polynomial x³+ 6x² + 4x + k is devisible by (x + 2) then the value of k is

1. -6
2. -7
3. -8
4. -10

Solution: The correct answer is 3. -8

⇒ x + 2 = 0, x = -2

∴ f (-2) = 0

⇒ or, (-2)² + 6 (-2)² + 4 (-2) + k = 0

⇒ or, -8 + 24 – 8 + k = 0

⇒ or, k = -8

The value of k is -8

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Example 7. In the polynomial f(x) if f(-\(\frac{1}{2}\)) =0 then the factor of f(x) will be

1. 2x – 1
2. 2x + 1
3. x – 1
4. x + 1

Solution: The correct answer is 2. 2x + 1

f(-\(\frac{1}{2}\))

∴ x = \(\frac{1}{2}\)

or, 2x + 1 = 0

The factor of f(x) will be 2x + 1.

Example 8. (x – 1) is a factor of the polynomial f(x) but it is not the factor of g(x). So (x – 1) will be a factor of

1. f(x) g(x)
2. – f(x) + g(x)
3. f(x) – g(x)
4. {f(x) + g(x)} g(x)

Solution: The correct answer is 1. f(x) g(x) (Product is the required answer)

Example 9. (x + 1) is a factor of xⁿ + 1 when

1. n is a positive odd integer
2. n is a positive even integer
3. n is a negative integer
4. n is a positive integer

Solution: The correct answer is 1. n is a positive odd integer

⇒ x + 1 = 0, x = -1

⇒ Now, (-1)ⁿ +1 = 0 n should be the positive odd integer.

Example 10. If n² – 1 is a factor of the polynomial an⁴ + bn³ + cn²+ dn + e then

1. a + c + e = b + d
2. a + b + e = c + d
3. a + b + c = d + e
4. b + c + d = a + e

Solution: The correct answer is a + c + e = b + d

⇒ n² = 1

⇒ n = ±1

∴ a (-1)⁴ + b (-1)³ + c (-1)² + d (-1) + e = 0

⇒ or, a – b + c – d + e = 0

⇒ or, a + c + e = b + d

Example 11. Which of the following is a polynomial?

1. \(\frac{x^2}{2}-\frac{2}{x^2}\)
2. \(\sqrt{2 x}-1\)
3. \(x^2+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}\)
4. \(\frac{x-1}{x+1}\)

Solution: The correct answer is 3. \(x^2+\frac{3 x^{\frac{3}{2}}}{\sqrt{x}}\)

\(x^2+3 x^{\frac{3}{2}-\frac{1}{2}}=x^2+3 x\)

 

Example 12. √2 is a polynomial of degree

1. 2
2. 0
3. 1
4. \(\frac{1}{2}\)

Solution: The correct answer is 2. 0

⇒ (√2 = √2x°)

Example 13. Degree of polynomial 4x⁴ + 0x³ + 0x⁵ + 5x + 7 is

1. 0
2. 1
3. Any natural no
4. Not defined

Solution: The correct answer is 3. Any natural no

Example 14. If p (x) = x² – 2√2x + 1, then p (2√2) is equal to

1. 0
2. 1
3. a√2
4. 8√2+1

Solution: The correct answer is 2. 1

⇒ P (2√2) = (2√2)² -2√2 – 2√2 + 1 = 8 – 8 + 1 = 1

Example 15. The value of the polynomial 5x – 4x² + 3, when x = -1 is

1. -6
2. 6
3. 2
4. -2

Solution: The correct answer is 1. -6

⇒ 5(-1) – 4(-1)² + 3 = -5 – 4 + 3 = -6