Quadratic Equation

To solve the problem, we need to find the sum of the roots of the quadratic equation .

1. Solving the Quadratic Equation:
The given quadratic equation is:
This can be factored as:
So, the roots are and .

2. Finding the Sum of the Roots:
The sum of the roots is:

Final Answer:
The sum of the roots is 0 (Option A).

To solve this question, we need to determine the value of when the roots of the quadratic equation are real and equal.

1. Given Equation:
The given quadratic equation is:

2. Condition for Real and Equal Roots:
For the roots of a quadratic equation to be real and equal, the discriminant ( ) must be zero. The discriminant is given by:

3. Applying the Discriminant Formula:
In the given equation, , , and . The discriminant is:

4. Setting the Discriminant to Zero:
For real and equal roots, the discriminant must be zero:

5. Solving for :

Final Answer:
Option (C) is correct.

To solve the problem, we need to find the value of such that the quadratic equation has equal roots.

1. Understanding the Condition for Equal Roots:
For a quadratic equation , the roots are equal if the discriminant is zero:

2. Identify the Coefficients:
Given equation:
Here, , , and

3. Apply the Discriminant Condition:

4. Solve for :

Final Answer:
The value of is for the equation to have equal roots.

To solve the problem, we need to find the value of such that the quadratic equation has two equal roots.

1. Understanding the Condition for Equal Roots:
For a quadratic equation to have two equal roots, its discriminant must be zero.

Discriminant

2. Identifying Coefficients:
From the equation , we have:
, ,

3. Applying the Discriminant Formula:

4. Solving the Equation:

Final Answer:
The value of is .

To solve the problem, we need to find the sum of the roots of the quadratic equation .

1. Understanding the Standard Form:
A quadratic equation in the form has the sum of its roots given by the formula:

2. Identify Coefficients:
From the given equation , we identify:

3. Applying the Formula:
Substitute the values of and into the sum formula:

Final Answer:
The sum of the roots is .

To solve the problem, we need to find the roots of the quadratic equation:

1. Understanding the Standard Form:

A quadratic equation is of the form:

Here, , , and

2. Using the Quadratic Formula:

The roots of a quadratic equation are given by:

Substituting the values:

3. Calculating the Two Roots:

Final Answer:

The roots of the equation are

To solve the problem, we need to find the value of , where and are the roots of the quadratic equation .

1. Understanding the Identity:
We use the identity:

2. Sum and Product of Roots:
For the quadratic equation , the sum and product of the roots are:

3. Apply the Identity:
Substitute the values into the identity:

4. Expressing with Common Denominator:
We take the LCM of the terms to combine them:

Final Answer:
The value of is .