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Quadratic equations

Written by Hassan Raza (Mathematics)

8 Class 11 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The roots of x² - 3x + 2 = 0 are:

    • 1 3 and 2
    • 2 1 and 2
    • 3 -1 and -2
    • 4 1 and -2
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    Correct answer: 1 and 2

    (x - 1)(x - 2) = 0.

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  2. If the roots of a quadratic are real and equal, the discriminant is:

    • 1 Negative
    • 2 Zero
    • 3 Positive
    • 4 Undefined
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    Correct answer: Zero

    b² - 4ac = 0 gives equal real roots.

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  3. If a and b are roots of x² - 5x + 6 = 0, then a + b equals:

    • 1 -6
    • 2 5
    • 3 6
    • 4 -5
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    Correct answer: 5

    Sum of roots = 5.

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  4. A quadratic with roots 2 and 3 is:

    • 1 x² - x + 6 = 0
    • 2 x² - 5x + 6 = 0
    • 3 x² - 6x + 5 = 0
    • 4 x² + 5x + 6 = 0
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    Correct answer: x² - 5x + 6 = 0

    x² - (sum)x + product = x² - 5x + 6.

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  5. The cube roots of unity are 1, w and w². The value of 1 + w + w² is:

    • 1 -1
    • 2 0
    • 3 3
    • 4 1
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    Correct answer: 0

    The sum of all cube roots of unity is 0.

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  6. Solve x² - 4x + 4 = 0.

    • 1 x = 2 (repeated)
    • 2 x = 4
    • 3 x = 2 or -2
    • 4 x = -2
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    Correct answer: x = 2 (repeated)

    (x - 2)² = 0.

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  7. If one root of x² - 5x + 6 = 0 is 2, the other is:

    • 1 3
    • 2 -3
    • 3 4
    • 4 -2
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    Correct answer: 3

    The product of roots is 6.

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  8. The complex cube roots of unity are:

    • 1 i and -i
    • 2 1 and -1
    • 3 2 and 3
    • 4 w and w²
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    Correct answer: w and w²

    They are the two non real roots of x³ = 1.

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