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The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:
The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:
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Practice Questions
1 question
Q1
The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:
3
4
2
6
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Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Questions & Step-by-step Solutions
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Q
Q: The sum of the roots of the quadratic equation 3x^2 - 12x + 9 = 0 is:
Solution:
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Steps: 8
Show Steps
Step 1: Identify the quadratic equation given, which is 3x^2 - 12x + 9 = 0.
Step 2: Recognize that a quadratic equation is in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Step 3: In our equation, a = 3, b = -12, and c = 9.
Step 4: Use Vieta's formulas, which tell us that the sum of the roots of the equation is given by the formula -b/a.
Step 5: Substitute the value of b (-12) and a (3) into the formula: -(-12)/3.
Step 6: Simplify the expression: -(-12) becomes 12, so we have 12/3.
Step 7: Calculate 12 divided by 3, which equals 4.
Step 8: Conclude that the sum of the roots of the quadratic equation is 4.
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