For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)
Practice Questions
1 question
Q1
For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)
6
11
1
0
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.
Questions & Step-by-step Solutions
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Q
Q: For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (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.
Steps: 5
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.
