Question

find the roots of the equation 5x² - 6x - 2 = 0 by the method of completing square.​

Answer 1

★ Given :

• 5x² - 6x - 2 = 0

★ To Find :

• Roots of the equation ?

★ Solution :

•Multiplying the equation throughout by 5, we get

$\implies{ \rm{25x ^{2} - 30x - 10 = 0}}$

• This is the same as :

${ \rm{ \implies{(5x)^{2} - 2 \times (5x) \times 3 + 3^{2} - 3^{2} - 10 = 0}}}$

$\implies{ \rm{(5x - 3)^{2} - 9 - 10 = 0}}$

$\implies{ \rm{(5x - 3)^{2} - 19 = 0}}$

$\implies{ \rm{(5x - 3) ^{2} = 19}}$

$\implies{ \rm{5x - 3 = ± \sqrt{19}}}$

$\implies{ \rm{5x = 3± \sqrt{19}}}$

$\implies{ \rm{x = \frac{3 \: ± \: \sqrt{19} }{5} }}$

${ \rm \implies{∴ The \: roots \: are \: \frac{3 + \sqrt{19} }{5} \: and \: \frac{3 - \sqrt{19} }{5}}}$

${ \rm{ \implies{Verify \: that \: the \: roots \: are { \red{ \: \frac{3 + \sqrt{19} }{5} \: and \: \frac{3 - \sqrt{19} }{5} }}}}}$