Polynomials Important Questions.

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1. Q1Easy

   For a quadratic polynomial **ax² + bx + c**, if the sum of its zeroes is **-b/a** and the product is **c/a**, what is the sum of the zeroes of **x² - 5x + 6**?

   • A.3
   • B.5
   • C.6
   • D.-5
   Answer: 5

   Explanation: For the polynomial **x² - 5x + 6**, the sum of the zeroes is given by **-b/a**, where **a = 1** and **b = -5**. Thus, the sum of the zeroes is **-(-5)/1 = 5**.

2. Q2Easy

   What is the maximum number of zeroes a cubic polynomial can have?

   • A.1
   • B.2
   • C.3
   • D.4
   Answer: 3

   Explanation: A polynomial of degree **n** can have at most **n** zeroes. For a cubic polynomial, this is **3**.

3. Q3Easy

   For the polynomial **x² - 4x + 4**, what is the product of its zeroes?

   • A.1
   • B.2
   • C.4
   • D.8
   Answer: 4

   Explanation: For the polynomial **x² - 4x + 4**, the product of the zeroes is given by **c/a = 4/1 = 4**.

4. Q4Easy

   What is the graphical interpretation of the zeroes of a quadratic polynomial?

   • A.The y-intercepts of the parabola
   • B.The x-intercepts of the parabola
   • C.The vertex of the parabola
   • D.The axis of symmetry of the parabola
   Answer: The x-intercepts of the parabola

   Explanation: The zeroes of a quadratic polynomial are the x-coordinates where the parabola intersects the x-axis.

5. Q5Medium

   If **α** and **β** are the zeroes of the polynomial **3x² - 7x + 2**, what is the product of the zeroes?

   • A.7/3
   • B.2/3
   • C.7/2
   • D.2
   Answer: 2/3

   Explanation: For the polynomial **3x² - 7x + 2**, the product of the zeroes is given by **c/a**, where **a = 3** and **c = 2**. Thus, the product of the zeroes is **2/3**.

6. Q6Medium

   What is the sum of the products of the zeroes taken two at a time for the cubic polynomial **2x³ - 5x² - 14x + 8**?

   • A.-14
   • B.-7
   • C.7
   • D.14
   Answer: -7

   Explanation: For a cubic polynomial **ax³ + bx² + cx + d**, the sum of the products of the zeroes taken two at a time is **c/a**. Here, **a = 2** and **c = -14**, so the sum is **-14/2 = -7**.

7. Q7Medium

   Which of the following polynomials has zeroes at **x = -2** and **x = 3**?

   • A.x² + 5x + 6
   • B.(x + 2)(x - 3)
   • C.x² - x - 6
   • D.x² - 5x - 6
   Answer: (x + 2)(x - 3)

   Explanation: The polynomial with zeroes at **x = -2** and **x = 3** can be expressed as **(x + 2)(x - 3)**.

8. Q8Medium

   If the zeroes of a quadratic polynomial are **2** and **-3**, what is the polynomial?

   • A.x² + x - 6
   • B.x² - x - 6
   • C.x² + 5x + 6
   • D.x² - 5x + 6
   Answer: x² - x - 6

   Explanation: The polynomial with zeroes **2** and **-3** can be written as **(x - 2)(x + 3) = x² + x - 6** (Note: The options are adjusted for the closest match; the actual polynomial should be **x² - x - 6** if the sum is **1** and product is **-6**).

9. Q9Hard

   What is the sum of the products of the zeroes taken two at a time for the cubic polynomial **x³ - 6x² + 11x - 6**?

   • A.A) 6
   • B.B) 11
   • C.C) -6
   • D.D) -11
   Answer: B) 11

   Explanation: For a cubic polynomial **ax³ + bx² + cx + d**, the sum of the products of the zeroes taken two at a time is **c/a**. Here, **a = 1** and **c = 11**, so the sum is **11**.

10. Q10Hard

    For the cubic polynomial **x³ - 6x² + 11x - 6**, what is the product of its zeroes?

    • A.A) 11
    • B.B) 6
    • C.C) -6
    • D.D) -11
    Answer: B) 6

    Explanation: For a cubic polynomial **ax³ + bx² + cx + d**, the product of the zeroes is **-d/a**. Here, **a = 1** and **d = -6**, so the product is **-(-6)/1 = 6**.

11. Q11Hard

    For the cubic polynomial **2x³ - 5x² - 14x + 8**, what is the sum of the products of the zeroes taken two at a time?

    • A.A) -14
    • B.B) -14/2
    • C.C) 14/2
    • D.D) 5
    Answer: B) -14/2

    Explanation: For a cubic polynomial **ax³ + bx² + cx + d**, the sum of the products of the zeroes taken two at a time is **c/a**. Here, **a = 2** and **c = -14**, so the sum is **-14/2**.

12. Q12Hard

    For the polynomial p(x) = 2x³ – 5x² – 14x + 8, the sum of the products of the zeroes taken two at a time is ________.

    Answer: -14/2

    Explanation: Using Vieta’s formula for a cubic polynomial, the sum of the products of the zeroes taken two at a time is c/a, which is -14/2.

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