Question: The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
Options:
2
3
4
5
Correct Answer: 4
Solution:
The sum of the roots is given by -b/a = 12/3 = 4.
The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
Practice Questions
Q1
The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
2
3
4
5
Questions & Step-by-Step Solutions
The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
Step 1: Identify the coefficients in the quadratic equation 3x^2 - 12x + 9 = 0. Here, a = 3, b = -12, and c = 9.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -b/a.
Step 3: Substitute the value of b (-12) and a (3) into the formula: -(-12)/3.
Step 4: Simplify the expression: 12/3 = 4.
Step 5: Conclude that the sum of the roots of the equation is 4.
Quadratic Equations – Understanding the properties of quadratic equations, specifically the relationship between coefficients and the sum of the roots.
Vieta's Formulas – Application of Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.
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