Question

For a given value of k,the products the roots of [x ^{2}-2kx+3k ^{2}-4=0 is 5 then roots may be characterized as ...............

Answer 1

\[x^2-2kx+3k^2-4=0\] us that what this says?

Answer 2

yews

Answer 3

plz help

Answer 4

gimme a second

Answer 5

u thr?

Answer 6

yeah thinking.

Answer 7

u hav gtalk?

Answer 8

when it says "characterized" what kind of answer? real? repeated? complex? what is the topic?

Answer 9

quadratics

Answer 10

it means its property

Answer 11

yeah i got that, i mean what kind of answer is expected?

Answer 12

it means its property

Answer 13

real or irrational like that

Answer 14

ok got it

Answer 15

product of roots is the constant, so
\[3k^2-4=5\]
\[3k^2=9\]
\[k^2=3\]
\[k=\pm\sqrt{3}\]

Answer 16

equation is
\[x^2-2\sqrt{3}x+5=0\] or
\[x^2+2\sqrt{3}+5=0\]

Answer 17

so.......

Answer 18

guess we don't have to characterize them, we can find them exactly.

Answer 19

u hav gtalk??plz give email id

Answer 20

there is chat here

Answer 21

bottom right

Answer 22

wel its slow

Answer 23

i hav many questions

Answer 24

actually pretty quick.
lets find the zeros ready?

Answer 25

is it real and distinct roots

Answer 26

we have solved for k and know it is
\[k=\sqrt{3}\] or
\[k=\sqrt{3}\]
so equation is
\[x^2-2\sqrt{3}x+5=0\] or
\[x^2+2\sqrt{3}x+5=0\] we solve the first one using formula get
\[x=\frac{2\sqrt{3}\pm+\sqrt{(2\sqrt{3})^2-4\times 1\times 5}}{2}\]
\[x=\frac{2\sqrt{3}\pm\sqrt{-8}}{2}\]
\[x=\frac{2\sqrt{3}\pm2\sqrt{2}i}{2}\]
\[x=\sqrt{3}\pm \sqrt{2}i\]

Answer 27

those are the solutions roots exactly. they are
\[\{\sqrt{3}+\sqrt{2}i,\sqrt{3}-\sqrt{2}i\}\]