Question

alpha by beta minus beta by alpha whole square​

Answer 1

Answer:

Let us Denote alpha as A and Beta as B

So we need to find what is A - B.

Quadratic Equation = ax² + bx + c

Let us consider a Quadratic Equation. If we find the sum of roots, A + B we would get it as:

A + B = -b / a

AB = c / a

Now we know that,

( A - B )² = ( A + B )² - 4 AB

=> ( A - B )² = ( -b / a )² - 4 ( -c / a )

=> ( A - B )² = ( b² / a² ) + 4 c / a

Taking LCM we get,

=> ( A - B )² = ( b² - 4ac ) / a²

Taking Square root on both sides we get,

=> A - B = √ [ ( b² + 4ac ) ] / a

Hence the value of A - B = √ ( b² - 4ac ) / a

it the answer I wish it helps you