Question

2x^2-x-3=0 by formula method and completing square method

Answer 1

Answer:

$\huge{\pink{\boxed{\green{\sf{x=-1,\frac{3}{2}}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

${\pink{\boxed{\green{\underline{\pink{\sf{METHOD(1)}}}}}}}$

${\pink{ \boxed{ \green{quadratic \: formula}}}} \\ \to 2{x}^{2} - x - 3 = 0 \\ \to d = {b}^{2} - 4ac \\ \to d = ({ - 1})^{2} - 4(2 \times - 3) \\ \to d = 1 - 4 ( - 6) \\ \to d = 1 + 24 \\ { \boxed{\to d = 25}} \\ \\ \to x = \frac{ -b± \sqrt{d} }{2a} \\ \to x = \frac{ - ( - 1)± \sqrt{25} }{2 \times 2} \\ \to x = \frac{1±5}{4} \\ \to x = \frac{ - 4}{4} \\ { \pink{ \boxed{ \green{\to x = - 1 }}}} - - - - - 1st \: zeroes \\ \to x = \frac{1 + 5}{4} \\ \to x = \frac{6}{4} \\ { \pink{ \boxed{ \green{\to x = \frac{3}{2} }}}} - - - - - 2nd \: zeroes$

${\pink{\boxed{\green{\underline{\pink{\sf{SECOND\:METHOD-}}}}}}}$

${ \pink{ \boxed{ \green{completing \: square \: method}}}} \\ \to2{x}^{2} - x - 3 = 0 \\ \to dividing \: both \: side \: by \: coefficient \: of \: {x}^{2} \\ \to {x}^{2} - \frac{x}{2} - \frac{3}{2} = 0 \\ \to both \: side \: adding \: (\frac{b}{2a} )^{2} = ({ \frac{ - 1}{2 \times 2} })^{2} = \frac{1}{16} \\ \to {x}^{2} - \frac{x}{2} + \frac{1}{16} = \frac{3}{2} + \frac{1}{16} \\ \to ({x - \frac{1}{4} })^{2} = \frac{24 + 1}{16} \\ \to x - \frac{1}{4} = \sqrt{ \frac{25}{16} } \\ \to x - \frac{1}{4} =± \frac{5}{4} \\ \to x = ± \frac{5}{4} + \frac{1}{4} \\ \to x = \frac{ - 5 + 1}{4} \\ \to x = \frac{ - 4}{4} \\ { \pink{ \boxed{ \green{\to x = - 1 }}}} - - - - - 1st \: zeroes \\ \to x = \frac{ 5 + 1}{4} \\ { \pink{ \boxed{ \green{\to x = \frac{3}{2} }}}} - - - - - 2nd \: zeroes$

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