**Finding the Roots of a Quadratic Polynomial**

To find the other root of the quadratic polynomial 2x - 3x + p = 0 and the value of p, we can use the fact that the sum of the roots of a quadratic polynomial is equal to the negative coefficient of the linear term divided by the coefficient of the quadratic term.

Let's start by finding the sum of the roots of the polynomial:

**Sum of the Roots Formula:**
The sum of the roots of a quadratic polynomial ax² + bx + c = 0 is given by the formula:
Sum of roots = -b/a

In this case, the polynomial is 2x - 3x + p = 0. Comparing this with the standard form ax² + bx + c = 0, we see that a = 2, b = -3, and c = p.

**Finding the Value of p:**
The sum of the roots is given by -b/a. Substituting the values, we have:
Sum of roots = -(-3)/2 = 3/2

Since we know that one root of the polynomial is 3, we can use the sum of roots formula to find the other root. Let's denote the other root as r.

**Using the Sum of Roots to Find the Other Root:**
The sum of the roots of a quadratic polynomial is equal to the negative coefficient of the linear term divided by the coefficient of the quadratic term. In this case, we have:
3 + r = 3/2
r = 3/2 - 3
r = -3/2

Therefore, the other root of the polynomial 2x - 3x + p = 0 is -3/2.

**Finding the Value of p:**
To find the value of p, we can substitute one of the roots into the polynomial equation and solve for p. Let's use the root r = -3/2.

Substituting r = -3/2 into the polynomial equation, we have:
2(-3/2) - 3(-3/2) + p = 0
-3 - (-9/2) + p = 0
-3 + 9/2 + p = 0
(-6 + 9)/2 + p = 0
3/2 + p = 0
p = -3/2

Therefore, the value of p is -3/2.

**Conclusion:**
The other root of the quadratic polynomial 2x - 3x + p = 0 is -3/2, and the value of p is -3/2.