The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value o

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Question: The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?

Options:

Correct Answer: 1

Solution:

The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.

The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?

The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?

Correct Answer: 1

Step 1: Identify the equation given, which is 2x^2 - 4x + k = 0.
Step 2: Recognize that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by the formula -b/a.
Step 3: In our equation, a = 2 and b = -4. Plug these values into the formula: -(-4)/2.
Step 4: Calculate -(-4)/2, which simplifies to 4/2 = 2. This means the sum of the roots is 2.
Step 5: We know from the problem that the sum of the roots should equal 3.
Step 6: Set the sum of the roots (2) equal to 3: 2 = 3. This is not correct, so we need to adjust k.
Step 7: To find the correct value of k, we need to adjust the equation so that the sum of the roots equals 3.
Step 8: The sum of the roots can also be expressed as (4 + k)/2 = 3, where k is the constant term.
Step 9: Solve for k: 4 + k = 6 (multiply both sides by 2), so k = 6 - 4.
Step 10: Therefore, k = 2.

Quadratic Equations – Understanding the properties of quadratic equations, specifically the relationship between coefficients and the sum of the roots.
Vieta's Formulas – Applying Vieta's formulas to find the sum of the roots of a quadratic equation.