What is the sum of the squares of the roots of the equation x^2 - 5x + 6 = 0?
Practice Questions
1 question
Q1
What is the sum of the squares of the roots of the equation x^2 - 5x + 6 = 0?
25
19
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The sum of the squares of the roots is given by (sum of roots)^2 - 2(product of roots). Here, sum = 5, product = 6. So, 5^2 - 2*6 = 25 - 12 = 13.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the sum of the squares of the roots of the equation x^2 - 5x + 6 = 0?
Solution: The sum of the squares of the roots is given by (sum of roots)^2 - 2(product of roots). Here, sum = 5, product = 6. So, 5^2 - 2*6 = 25 - 12 = 13.
Steps: 11
Step 1: Identify the equation given, which is x^2 - 5x + 6 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c.
Step 3: Identify the coefficients: a = 1, b = -5, c = 6.
Step 4: Calculate the sum of the roots using the formula -b/a. Here, sum = -(-5)/1 = 5.
Step 5: Calculate the product of the roots using the formula c/a. Here, product = 6/1 = 6.
Step 6: Use the formula for the sum of the squares of the roots: (sum of roots)^2 - 2(product of roots).
Step 7: Substitute the values: (5)^2 - 2*(6).
Step 8: Calculate (5)^2 = 25.
Step 9: Calculate 2*(6) = 12.
Step 10: Subtract: 25 - 12 = 13.
Step 11: Conclude that the sum of the squares of the roots is 13.
