Question

find roots of the following quadratic equations by factorization method, 2ax^2-(2a-b^2)x-b^2=0​

Answer 1

$\blue\ast\tt{ \: Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\ast\small\tt\blue{ \: By \: Factorisation \: Method}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue\ast\small \tt{ \: {2ax}^{2} - (2a - {b}^{2})x - {b}^{2} = 0 }$

$\blue\ast \small \tt{ \: {2ax}^{2} - 2ax - {b}^{2}x - {b}^{2} = 0 }$

$\blue\ast \small \tt{ \: 2ax(x - 1) - {b}^{2}(x - 1) = 0 }$

$\blue\ast\small \tt{ \: (x - 1)( 2ax - {b}^{2}) = 0 }$

$\ast\small \tt \blue{ \: (x - 1) = 0 }$

$\boxed{ \ast \: \small \tt \blue {x = 1 }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\ast \: \small \tt \blue{ 2ax - {b}^{2} = 0 }$

$\small\boxed{ \ast \: \small \tt \blue{x = \frac{ {b}^{2} }{2a}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue\ast\small\tt{ \: Roots \: are \: 1 \: and \: \frac{ {b}^{2} }{2a} }$

Answer 2

hope it's helpful for you