Question

please answer.............,......

Answer 1

Given Equation is 2x^2 + x - 4 = 0

= > x^2 + x/2 - 4/2 = 0

= > x^2 + x/2 - 2 = 0

= > x^2 + x/2 - 2 + (1/4)^2 - (1/4)^2 = 0

= > x^2 + x/2 + (1/4)^2 - 2 - (1/4)^2 = 0

= > (x +1/4)^2 = 2 + (1/4)^2

= > (x + 1/4)^2 = 2 + 1/16

= > (x + 1/4)^2 = 33/16

$= \ \textgreater \ (x + \frac{1}{4} ) = \frac{ \sqrt{33} }{4}$

Now,

(1)

$= \ \textgreater \ x + \frac{1}{4} = \frac{ \sqrt{33} }{4}$

$= \ \textgreater \ x = \frac{ \sqrt{33} }{4} - \frac{1}{4}$

$= \ \textgreater \ x = \frac{ \sqrt{33} - 1 }{4}$



(2)

$= \ \textgreater \ x + \frac{1}{4} = - \frac{ \sqrt{33} }{4}$

$= \ \textgreater \ x = -\frac{ \sqrt{33} }{4} - \frac{1}{4}$

$= \ \textgreater \ x = \frac{ -\sqrt{33} - 1 }{4}$


Therefore, the roots of the equation are:

$x = \frac{ \sqrt{33} - 1 }{4} , x = \frac{- \sqrt{33} - 1 }{4}$



Hope this helps!

Answer 2

Hi,

Please see the attached file!



Thanks