What is the value of alpha minus beta
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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
Step-by-step explanation:
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