Sum of the roots of the quadratic equation= -b/a

Given,
a= 3, b= ( -9)

-b/a = - (-9) /3 = 9/3= 3

Therefore, answer is 3

Solution:

To find the sum of the roots of a quadratic equation, we can use the formula:

Sum of roots = - (coefficient of x term) / (coefficient of x² term)

Given quadratic equation: 3x² - 9x + 5 = 0

Step 1: Identify the coefficients
- Coefficient of x² term = 3
- Coefficient of x term = -9
- Constant term = 5

Step 2: Apply the formula to find the sum of roots
Sum of roots = - (-9) / 3
= 9 / 3
= 3

Therefore, the sum of the roots of the given quadratic equation is 3.

Explanation:

To understand why the sum of the roots can be found using the formula, we need to consider the nature of a quadratic equation.

A quadratic equation is of the form ax² + bx + c = 0, where a, b, and c are constants.

When we solve a quadratic equation, we find the values of x that satisfy the equation. These values are called the roots of the equation.

The quadratic formula provides a way to find the roots of any quadratic equation: x = (-b ± √(b² - 4ac)) / (2a)

From this formula, we can see that the roots of the equation are dependent on the coefficients a, b, and c.

The sum of the roots can be found by adding the values of x obtained from the quadratic formula.

To simplify the process, we can use the fact that the sum of the roots is equal to the negation of the coefficient of the x term divided by the coefficient of the x² term.

This can be derived by comparing the quadratic formula with the standard form of a quadratic equation.

In our case, the coefficient of the x term is -9 and the coefficient of the x² term is 3.

Using the formula, we can calculate the sum of the roots as -(-9) / 3 = 9 / 3 = 3.

Therefore, the sum of the roots of the given quadratic equation is 3.

Summary:
- The sum of the roots of a quadratic equation can be found using the formula: Sum of roots = -(coefficient of x term) / (coefficient of x² term)
- Applying this formula to the given quadratic equation 3x² - 9x + 5 = 0, we find that the sum of the roots is 3.