Quadratic equation: roots PLEASE HELP! (1 Viewer)

[azn 2245]

The question is: "One root of the quadratic equation 4x^2-24x+k=0 is twice the other root. Determine k" I have no idea how to do these type of questions Could someone please help me?

 

[Graceofgod]

The question is: "One root of the quadratic equation 4x^2-24x+k=0 is twice the other root. Determine k" I have no idea how to do these type of questions Could someone please help me?

x = [-24 + root(24^2 - 4*4*k)]/8 or x = [-24 - root(24^2 - 4*4*k)]/8

These are the roots. Now, one has to equal double the other.

Let root(24^2 - 4*4*k) = m

Therefore:

[-24 + m]/8 = [-24 - m)]/4
-24 + m = -48 - 2m
m = -8

or

[-24 + m]/4 = [-24 - m]/8
-48 + 2m = -24 - m
m = 8

Therefore root(24^2 - 4*4*k) = +/- 8
576 - 16k = 64
k = 32

I think that is right.

EDIT: Prob a simpler way to do it, so if that doesn't make sense, wait for someone else to correct me.

EDIT: Just checked that answer, its wrong lol. Hmm, yep wait for someone else to correct me.

EDIT: I found an error, its all good now I think.

 

[laureese]

um i kinda suck at maths myself but ill take a stab at it for the sake of studying..

4x^2 - 24x + K = 0

Let the roots be; a and 2a ( i actually mean alpha)

a + 2a = -b/a
3a = 24/4
3a = 6
:. a = 2

a x 2a = c/a
2a^2 = K/4
sub in a = 2 (from above)
2 x (2)^4 = K/4
8 = K/4
:. K = 4 x 8
= 32

 

[laureese]

shit well i got a different answer to the person above.. so i dunno anymore


... but they changed it now..

 

[nandayo]

um i kinda suck at maths myself but ill take a stab at it for the sake of studying..

4x^2 - 24x + K = 0

Let the roots be; a and 2a ( i actually mean alpha)

a + 2a = -b/a
3a = 24/4
3a = 6
:. a = 2

a x 2a = c/a
2a^2 = K/4
sub in a = 2 (from above)
2 x (2)^4 = K/4
8 = K/4
:. K = 4 x 8
= 32

That's what I got...

 

[azn 2245]

to the first reply: thanks for the help, but i really dont understand how you got the answer

 

[nandayo]

The question tests your knowledge on the sum and differences of roots - this should be a chapter in your textbook. Basically if the roots of an equation are α and β (alpha and beta) it's proven that: αβ = c/a and α+β = -b/a. Using the values of the equation and because you know that α=2β (as the question said one roots is twice the other) you can work out the value of k as shown above.

 

[Graceofgod]

to the first reply: thanks for the help, but i really dont understand how you got the answer

Using quadratic formula? Copy and paste the parts you don't get.

I appologise to anyone who got confused, I made a minor multiplication error.

 

[azn 2245]

its cool, i now understand how it works thankyou everyone for helping!!!!! And good luck in the HSC!

 

[Graceofgod]

shit well i got a different answer to the person above.. so i dunno anymore

Your answer is better. I never bothered to learn all that stuff. This is just the way I do maths

Derive the formulas in the test

 

[tommykins]

The question is: "One root of the quadratic equation 4x^2-24x+k=0 is twice the other root. Determine k" I have no idea how to do these type of questions Could someone please help me?

another way to do it is -

let roots be a and 2a

Sum of roots 3a = 6 , a = 2

sub x = 2 into the equation.

4.2^2 - 24.2 + k = 0
16 - 48 + k = 0
-32 + k = 0
k= 32

 

[Graceofgod]

another way to do it is -

let roots be a and 2a

Sum of roots 3a = 6 , a = 2

sub x = 2 into the equation.

4.2^2 - 24.2 + k = 0
16 - 48 + k = 0
-32 + k = 0
k= 32

Ah yes. I need to go back and study this topic. I never actually did it.

But yes, this is the best way to do it. Sorry.

 

[crammy90]

sub x = 2 into the equation.

if a = 2 and then we sub a's value for x in the equation, does this mean in an equation x = a? and what does the beta stand for in the equation