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Quiz Chapter 2: Quadratic Functions

10 questions · Form 4 Additional Mathematics Bab 1: Quadratic Functions

Question 1 of 10Score: 0

If α and β are roots of 2x² - 6x + 3 = 0, find the value of α + β.

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. If α and β are roots of 2x² - 6x + 3 = 0, find the value of α + β.

  1. -3
  2. 3
  3. 32
  4. -32
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Answer: B

Sum of roots α + β = -ba = --62 = 62 = 3.

2. If α and β are the roots of x² - 5x + 2 = 0, evaluate α² + β².

  1. 21
  2. 25
  3. 29
  4. 23
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Answer: A

SOR α + β = 5, POR αβ = 2. Use identity: α² + β² = (α + β)² - 2αβ = (5)² - 2(2) = 25 - 4 = 21.

3. Find the roots of the quadratic equation 2x² - 5x - 3 = 0.

  1. x = 3 or x = -12
  2. x = -3 or x = 12
  3. x = 3 or x = 12
  4. x = -3 or x = -12
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Answer: A

Factorising gives (2x + 1)(x - 3) = 0 => 2x + 1 = 0 or x - 3 = 0 => x = -12 or x = 3.

4. Find the quadratic equation whose roots are reciprocal to the roots of 3x² - 7x + 2 = 0.

  1. 2x² - 7x + 3 = 0
  2. 3x² + 7x + 2 = 0
  3. 2x² + 7x + 3 = 0
  4. 7x² - 3x + 2 = 0
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Answer: A

Roots of original equation: SOR = 73, POR = 23. For reciprocal roots 1/α and 1/β: New SOR = (α+β)/(αβ) = (73)/(23) = 72. New POR = 1/(αβ) = 32. Equation: x² - (72)x + 32 = 0 => 2x² - 7x + 3 = 0.

5. Find the minimum value of the quadratic function f(x) = 2(x + 1)² - 9.

  1. -1
  2. -9
  3. 2
  4. 9
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Answer: B

In vertex form f(x) = a(x - h)² + k with a = 2 > 0, the minimum value is given directly by k, which is -9.

6. Solve the quadratic inequality x² - 4x - 5 < 0.

  1. x < -1 or x > 5
  2. -1 < x < 5
  3. -5 < x < 1
  4. x < -5 or x > 1
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Answer: B

Factorise: (x + 1)(x - 5) < 0. Critical values are x = -1 and x = 5. For '< 0', the solution is between the roots: -1 < x < 5.

7. Find the range of values of k for which the equation x² + 4x + k = 0 has two distinct real roots.

  1. k < 4
  2. k > 4
  3. k ≤ 4
  4. k = 4
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Answer: A

Two distinct roots require b² - 4ac > 0 => (4)² - 4(1)(k) > 0 => 16 - 4k > 0 => 4k < 16 => k < 4.

8. The graph of f(x) = ax² + bx + c does NOT intersect the x-axis. Which statement must be TRUE?

  1. b² - 4ac > 0
  2. b² - 4ac = 0
  3. b² - 4ac ≥ 0
  4. b² - 4ac < 0
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Answer: D

No intersection with the x-axis means the quadratic equation f(x) = 0 has no real roots, so b² - 4ac < 0.

9. State the y-intercept of the quadratic graph f(x) = -2(x - 1)² + 8.

  1. (0, 8)
  2. (0, 6)
  3. (0, -2)
  4. (0, 10)
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Answer: B

y-intercept occurs when x = 0: f(0) = -2(0 - 1)² + 8 = -2(1) + 8 = 6. Thus, y-intercept is (0, 6).

10. The quadratic function f(x) = -(x - 3)² + 7 has a turning point at (h, k). State the coordinates and nature of the turning point.

  1. Minimum point at (3, 7)
  2. Maximum point at (-3, 7)
  3. Maximum point at (3, 7)
  4. Minimum point at (-3, 7)
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Answer: C

Since a = -1 < 0, the graph is maximum shaped (∩). From f(x) = a(x - h)² + k, vertex is (h, k) = (3, 7).

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