Question

The equation 2x 2 −62x+k=0 has two real roots, one of which is 1 more than twice the other. Find the value of k .

Answer 1

\[2x^{2}- 62x + k = 0\]

Answer 2

help me

Answer 3

let m, n are roots,m -1=2n
and you have formula m +n = -b/a
and m*n = c/a
replace and solve for m, n

Answer 4

please what are the roots confusion

Answer 5

soorry

Answer 6

ohh wait help come backkkk

Answer 7

@Loser66

Answer 8

Do you mean what are roots, or what are the answers?

Answer 9

no the roots not the answer i was wondering how is that related to the answer
too I would never ask for theanswer just walk me through thats all

Answer 10

if u give me the answer thats just like saying im dumb I hate it

Answer 11

Well, the roots of an equation is another way of saying the zeros.

Answer 12

Could just identify the roots in the problem plz

Answer 13

:)

Answer 14

In the problem, they are a range because of the k and the conditions. They are not individual values.

Answer 15

Or... hmmm...

Answer 16

"has two real roots, one of which is 1 more than twice the other. Find the value of k ."

OK. Read that wrong at first... not a range. Those are two distinct values.

Answer 17

All i though is the anwer is between the interger valus 0 to 900

Answer 18

I mean 999

Answer 19

hmm... this is super hard but I love it

Answer 20

OK, so if you have these roots, \(r_0\) and \(r_1\), that thing is saying that:
\(r_0=?\) and \(r_1=2(r_1)+1\) Now, because keeping track of sub this and sub that is a pain, and because +1 on one side is the same as -1 on the other, L66 wrote that as:
Let m and n be the roots where:
m -1=2n

Answer 21

when u have (x-r1)(x-r2), they should give you the original equation

Answer 22

Yes.

Answer 23

okay so how do use this to get the answer

Answer 24

WAIT, there's a far easier way to do this using the quadratic formula/discriminants

Answer 25

Another thing L66 was pointing out was a relationship between the roots and the positions of things in the equation.

Remember that these things are in the form of:
\(ax^{2}+bx + c = 0\)

Answer 26

I believe that using the quadratic formula would be far faster and easier to understand
\[2(62-\sqrt{62*62-8k})/4+1=(62+\sqrt{62*62-8k})/4\]

Answer 27

just solve for k in that equation

Answer 28

oh im dumb actually

Answer 29

okay hold wait sec plz im dumber than

Answer 30

okay, in an quadratic where r and s are the roots, then k in the equation is just rs
so far so good?

Answer 31

keeping with the previous equation, (realized that im not that dumb lol)
just solve for \[\sqrt{62*62-8k}\] , as a 1 unknown algebra equation

Answer 32

32 - 8k + 1 = 32 - 8k

Answer 33

oh wow after the trouble

Answer 34

note that one is + and the other is -

Answer 35

wait than wont k be 0

Answer 36

Umm... I thinkl you just skipped the condition on the roots and their relationship.

Answer 37

I'm getting k as 420

Answer 38

he did

Answer 39

let a be the sqrt(stuff)

the u have 2*(62-a)/4 +1 = (62+a)/4

Answer 40

i going check it its right than i goign write u a testmonial if its wrong all the credit goes to @e.mccormick

Answer 41

He got the right answer. Hmm.

Answer 42

theres also another k answer i believe

Answer 43

no wait im dumb lol

Answer 44

With those conditions, it would be hard to get 2. LOL

Answer 45

I went in imaginary by accident lol

Answer 46

so it 420 right

Answer 47

Ah, but you mean if the \(\pm\) is reversed.

Answer 48

im checking okay

Answer 49

yah @e.mccormick

Answer 50

but its just the negative of the answer, so the square is the same

Answer 51

Alright 420 was right sorry i got these problems for brilliant

Answer 52

wow that took more effort than expected lol

Answer 53

Got brilliant it hard to get these answers

Answer 54

Now, to use \(ax^{2}+bx + c = 0\) with \(2x^{2}- 62x + k = 0\)

m*n=k/2
m+n=62/2
m = 2n+1

(2n+1)*n=k/2
2n+1+n=62/2

(2n+1)*n=k/2
3n=30
n=10

(2(10)+1)*10=k/2

(21)*10=k/2

210=k/2
420=k

That was where I was going.....