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Polynomials Test - 4

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Polynomials Test - 4
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Weekly Quiz Competition
  • Question 1
    1 / -0

    Which of the following expressions is a zero polynomial?

    Solution

    '0' is a zero polynomial.

     

  • Question 2
    1 / -0

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

    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 3
    1 / -0

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

    Solution

    Product of zeroes = -1/6

     

  • Question 4
    1 / -0

    Which of the following expressions is a constant polynomial?

    Solution

    We can write 2 = 2 × 1 = 2 × x°
    Therefore, 2 is a constant polynomial as power of variable x is zero.

     

  • Question 5
    1 / -0

    Which of following polynomials has 5 as a zero?

    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 6
    1 / -0

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

    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 7
    1 / -0

    What will be the positive zero of the polynomial x2 + 3x – 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 8
    1 / -0

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

    Solution

    2x2 + x – 10 = 0
    2x2 + 5x – 4x – 10 = 0,

    x(2x + 5) – 2 (2x + 5) = 0,
    (x – 2) (2x + 5) = 0,

    ⇒ x = 2, -5/2
    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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