Question

What Is Formula For Alpha minus Beta

(α-β)?

Answer 1

$\mathfrak{The\:Answer\:is}$


Let us Denoted 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 = √ [ -1 ( b² + 4ac ) ] / a

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



$\boxed{Hope\:This\:Helps}$

Answer 2

Heya !

Merry Christmas

$<b><u>Here Is Your Answer:----</u></b>$

$<b><u>Let us Denoted alpha as A and Beta as B$

$So we need to find what is A - B.$

$Quadratic Equation = {ax}^{2} + bx + c$

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

$A + B = -b / a$

$AB = c / a$

$Now we know that,$

${( A - B )}^{2} ={ ( A + B )}^{2} - 4 AB$

$=> {( A - B )}^{2}={ ( -b / a )}^{2} - 4 ( c / a )$

$=>{ ( A - B )}^{2} = ( {-b}^{2} / {a}^{2} ) - 4 c / a$

$Taking\: LCM\: we\: get, [tex]=> {( A - B )}^{2} = ( {-b}^{2} - 4ac ) / {a}^{2}$

$Taking \:Square\: root \:on\: both \:sides \:we \:get,$

$\implies A - B = \sqrt {[ -1 ( {b}^{2} + 4ac ) ] / a}$

$Hence the value of A - B = \sqrt( {-b}^{2} - 4ac ) / a$

Hope the answer helped !

Kindly Mark Brainliest If Helped :)