Question

if one root of the equation
$2x {}^{2} + kx + 4 = 0$
is 2 then what is the other root
​

Answer 1

Step-by-step explanation:

Hello!

Hello!let's solve this beautiful Question!

2x^2 + kx +4 = 0

from here,

2(4) + k(2) +4 = 0

2 is root so it will satisfy equation

2k = -12

k = (-6)

So our improved equation is,

2x^2 - 6x +4 = 0

let,

$\alpha \: and \: \beta \: be \: roots \: of \: equation \\ from \: where \: \alpha = 2$

$we \: know \: that \: \\ \alpha + \beta = \frac{ - b}{a}$

$( \alpha + \beta ) = 3$

$now \: put \: \alpha = 2 \: in \: above \: equation$

$when \: we \: put \: \alpha = 2 \\ we \: get \: \beta \: as \: 1$

$so \: roots \: are \: \alpha = 2 \\ another \: root(answer \: root) = 1$

Hope it helps uh!

Answer 2

Answer:

Let other root be x

2x^2+Kx+4=Let

sum of the roots= x+2 =-k/2.....1

product of roots=2x=4/2......2

2x=4/2

=2x=2

x=1

from (1)

x+2=-k/2

1+2=-k/3

3=-k/3

k=-9

hence other root of the equation is 1