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For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (20

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Question: For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)

Options:

  1. 6
  2. 11
  3. 1
  4. 0

Correct Answer: 6

Exam Year: 2019

Solution: 

The product of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -d/a. Here, d = -6 and a = 1, so the product is -(-6)/1 = 6.

For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (20

Practice Questions

Q1
For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)
  1. 6
  2. 11
  3. 1
  4. 0

Questions & Step-by-Step Solutions

For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)
  • Step 1: Identify the coefficients of the cubic equation x^3 - 6x^2 + 11x - 6 = 0. Here, a = 1, b = -6, c = 11, and d = -6.
  • Step 2: Recall the formula for the product of the roots of a cubic equation, which is given by -d/a.
  • Step 3: Substitute the values of d and a into the formula. Here, d = -6 and a = 1.
  • Step 4: Calculate the product of the roots: -(-6)/1 = 6.
  • Step 5: Conclude that the product of the roots of the equation is 6.
  • Vieta's Formulas – The relationship between the coefficients of a polynomial and the sums and products of its roots.
  • Cubic Equations – Understanding the structure and properties of cubic equations, including how to identify coefficients.
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