Question

If on of the roots of mx^2 + (4m-1)x + k = 0 is -1-2i, where m and k are real numbers. What is the value of K. I'm getting the equation for -1-2i but I keep getting k = 5 rather than the correct answer k= 5/2. PLease help! Thanks !

Answer 1

(x+1)^2 -(2i)^2
x^2+2x+1 + 4
x^2+2x+5
so
4m-1 = 2
wait.

Answer 2

u got x^2+2x+5=0 right ?

Answer 3

yes

Answer 4

there is another longer method,
since -1-2i is the root, it must satisfy the equation
so put x=-1-2i in mx^2 + (4m-1)x + k = 0
what u get ?
then equate real and imaginary parts

Answer 5

How do you equate real and imaginary parts?

Answer 6

1st did u put x=-1-2i in mx^2 + (4m-1)x + k = 0

Answer 7

Oh no I did not

Answer 8

I plugged it in but now what do I do?

Answer 9

mx^2 + (4m-1)x + k = 0
m(-1-2i)^2 + (4m-1)(-1-2i) + k = 0
m(1-4-4i) + (-4m-8mi+1+2i) + k=0
can u write next few steps of simplification ?

Answer 10

-7m-8mi+1+2i +k

Answer 11

-4mi -8mi = -12 mi

Answer 12

so u get
-7m-12mi+1+2i +k=0

Answer 13

Ok ok then what do we do?

Answer 14

(-7m+1+k) + i (-12m+2) = 0
real part = -7m+1+k = 0
imaginary part = -12m+2 = 0 <----find m from here

Answer 15

m(-1-2i)^2 wouldn't it be m(-3+4i) ? you put m(1-4-4i)

Answer 16

oh wait! my bad, so sorry. its m(-3+4i) only.

Answer 17

-7m-4mi+1+2i +k=0
u get
-4m+2=0 <----find m from here

Answer 18

did u get m= 1/2 ?
then put that in
-7m+1+k = 0
to get k=5/2

Answer 19

ask if u did not understand any step.

Answer 20

I see what you did! Thank you hartnnn I'm getting the hang of this

Answer 21

welcome ^_^
did u understand equating real and imaginary part ?

Answer 22

Yes! Cause a+bi right

Answer 23

yes, if a+bi =0 = 0+0i
then a=0 and b=0

Answer 24

Thanks man! Very very helpful :)

Answer 25

You're awesome at math. Hope to be like you one day lol

Answer 26

with practice , you can become better than me :)

Answer 27

:) have a good night or day man

Answer 28

same to u :)