If the sum of the roots of the equation x^2 - 3x + k = 0 is 3, what is the value

If the sum of the roots of the equation x^2 - 3x + k = 0 is 3, what is the value of k? (2021)

If the sum of the roots of the equation x^2 - 3x + k = 0 is 3, what is the value of k? (2021)

Step 1: Identify the equation given, which is x^2 - 3x + k = 0.
Step 2: Recall the formula for the sum of the roots of a quadratic equation ax^2 + bx + c = 0, which is -b/a.
Step 3: In our equation, a = 1 and b = -3. So, the sum of the roots is -(-3)/1.
Step 4: Calculate the sum of the roots: -(-3) = 3, and 3/1 = 3.
Step 5: We know from the question that the sum of the roots is 3, which matches our calculation.
Step 6: Now, we need to find the value of k. The sum of the roots can also be expressed as 3 = 3 - k.
Step 7: Rearranging the equation gives us k = 3 - 3.
Step 8: Calculate k: k = 0.

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 relate the coefficients of a polynomial to sums and products of its roots.