Formula of Alpha plus Beta Whole Square

The formula for Alpha plus Beta whole square is an important formula in mathematics. It's used in various mathematical equations, especially in quadratic equations. The formula can be derived using the identity (a+b)² = a² + 2ab + b².

Explanation of the Formula

The formula for Alpha plus Beta whole square is given as:

(a + b)² = a² + 2ab + b²

Where a and b are any two real numbers. Here, Alpha and Beta are the roots of a quadratic equation.

Derivation of the Formula

Let's consider a quadratic equation:

ax² + bx + c = 0

Here, Alpha and Beta are the roots of the quadratic equation. We can write the equation as:

x² - (Alpha + Beta)x + AlphaBeta = 0

Now, we need to find the sum of the roots of the quadratic equation, which is given by:

Alpha + Beta = -b/a

We can square both sides of the equation to get:

(Alpha + Beta)² = (-b/a)²

Multiplying both sides by a², we get:

a²(Alpha + Beta)² = b²

Expanding the left-hand side of the equation, we get:

a²(Alpha² + 2AlphaBeta + Beta²) = b²

Substituting AlphaBeta = c/a, we get:

a²(Alpha² + 2c/a + Beta²) = b²

Simplifying the equation, we get:

Alpha² + 2c/a + Beta² = b²/a²

Multiplying both sides by a², we get:

a²Alpha² + 2ac + a²Beta² = b²

Substituting (a²Alpha² + a²Beta²) = (a + b)² - 2ac, we get:

(a + b)² = b² - 2ac

Thus, we have derived the formula for Alpha plus Beta whole square.

Conclusion

In conclusion, the formula for Alpha plus Beta whole square is essential in solving various mathematical equations, especially quadratic equations. The derivation of the formula involves using the quadratic equation's roots and squaring the sum of the roots. The formula is (a + b)² = a² + 2ab + b², where a and b are any two real numbers, and Alpha and Beta are the roots of a quadratic equation.