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

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

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

Step 1: Identify the equation given, which is x^2 - 3x + p = 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 = 1 and b = -3.
Step 4: Substitute the values of a and b into the formula: -(-3)/1.
Step 5: Calculate -(-3)/1, which simplifies to 3/1 = 3.
Step 6: Since the sum of the roots is already given as 3, this means our calculation is correct.
Step 7: Notice that the value of p does not affect the sum of the roots, so p can be any value.

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