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

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.

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