See.... first of all ax^2 -bx + c =0 hoga .... aur calculate kya krna h .... i mean alpha aur beta ke beech kuch to hoga like + or - ....

Quadratic Equation and its Roots:
A quadratic equation is a polynomial equation of degree 2. It can be written in the general form as ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable. The roots of a quadratic equation are the values of x that satisfy the equation and make it equal to zero.

Using the Quadratic Formula:
To find the roots of a quadratic equation, we can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the coefficients of the quadratic equation ax^2 + bx + c = 0 into the formula, we can calculate the roots.

Finding Alpha and Beta:
Given the quadratic equation ax^2 - bx + c = 0, we can use the quadratic formula to find the roots.

The roots are denoted as alpha (α) and beta (β). Let's calculate them step by step:

1. Calculate the Discriminant:
The discriminant (Δ) of a quadratic equation is the expression inside the square root in the quadratic formula. It helps determine the nature of the roots.

The discriminant is given by: Δ = b^2 - 4ac

2. Check the Nature of the Roots:
The nature of the roots depends on the value of the discriminant:
- If Δ > 0, the equation has two distinct real roots.
- If Δ = 0, the equation has two identical real roots.
- If Δ < 0,="" the="" equation="" has="" two="" complex="" />

3. Calculate Alpha and Beta:
Based on the nature of the roots, we can calculate alpha and beta as follows:
- If the roots are real and distinct (Δ > 0), then:
alpha = (-b + √Δ) / (2a)
beta = (-b - √Δ) / (2a)
- If the roots are real and identical (Δ = 0), then:
alpha = beta = -b / (2a)
- If the roots are complex (Δ < 0),="" />
alpha = (-b + i√|Δ|) / (2a)
beta = (-b - i√|Δ|) / (2a)

Summary:
In summary, to find the roots of a quadratic equation ax^2 - bx + c = 0, you can use the quadratic formula to calculate the discriminant (Δ). Based on the value of the discriminant, you can determine the nature of the roots and then calculate the values of alpha (α) and beta (β) accordingly.