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

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

Options:

Correct Answer: 2

Solution:

Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.

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

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

Step 1: Identify the quadratic equation given, which is 2x^2 - 4x + k = 0.
Step 2: Recall the formula for the sum of the roots of a quadratic equation, which is -b/a.
Step 3: In the equation, identify the values of a and b. Here, a = 2 and b = -4.
Step 4: Substitute the values of a and b into the sum of roots formula: -(-4)/2.
Step 5: Calculate -(-4)/2, which simplifies to 4/2 = 2. This means the sum of the roots is 2.
Step 6: We know from the question that the sum of the roots is also equal to 3.
Step 7: Set the sum of the roots equal to 3: 2 + 1 = 3.
Step 8: From the equation 2 + 1 = 3, we find that the missing value is 1, which is the value of k.

Sum of Roots of Quadratic Equations – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by the formula -b/a.
Understanding Coefficients – Recognizing the coefficients a, b, and c in the context of the quadratic equation.
Solving for Unknowns – Finding the value of k based on the given condition about the sum of the roots.