What is the value of a to have double solutions in this quadratic equation?

[kreshnik]

Homework Statement

How should be the value of a so quadratic equation $$ax^2-4x+4=0$$ to have double solutions?
$$A)\;\;2$$
$$B)\;\;1$$
$$C)\;-1$$
$$D)\;-2$$

Homework Equations

The Attempt at a Solution

$$D=b^2-4ac$$
If:
$$D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}$$
$$D=0\;\;\rightarrow\; {x_1}\;\rightarrow\;\text{only one solution}$$
$$D<0\;\;\rightarrow\; \text{no solution.}$$

so:
$$(-4)^2-4*a*4=16-16*a$$
$$\text{If:}\;\;a=-1\;\;\rightarrow\;D=32$$
$$\text{If:}\;\;a=-2\;\;\rightarrow\;D=48$$

Which one should be?? thank you.

 

[LearninDaMath]

Looks like both C and D work. Are you only allowed to choose one answer?

 

[checkitagain]

How should be the value of a so quadratic equation
$$ax^2-4x+4=0$$ to have

----> double <---- solutions?

$\text{No, this word is misleading and must be instead be}$
$\text{meant for the solution to be repeated, and not be "double,"}$
$\text{as in two different solutions.}$


$$A)\;\;2$$
$$B)\;\;1$$
$$C)\;-1$$
$$D)\;-2$$

Homework Equations

The Attempt at a Solution

$$D=b^2-4ac$$
If:
$$D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}$$
$$D=0\;\;\rightarrow\; {x_1}\;\rightarrow\;\text{only one solution}$$
$$D<0\;\;\rightarrow\; \text{no solution.}$$

so:
$$(-4)^2-4*a*4=16-16*a$$
$$\text{If:}\;\;a=-1\;\;\rightarrow\;D=32$$
$$\text{If:}\;\;a=-2\;\;\rightarrow\;D=48$$

Which one should be?? thank you.

"Double" here should mean the solutions are twins.


So, you need D = 0, so that there is a repeated solution.

$So, \ set \ \ 16 - 16a \ \ equal \ to \ 0 \ and \ solve$

$\ for \ that \ value \ of \ a.$


*** Edit


That means that a = 1.

So, the answer is B.



***2nd edit:

Curious3141 repeated the essence of what I already stated.

 

[Curious3141]

Terrible question. "Double solutions" is nonsensical. It's either "distinct real roots" for D>0 or "single repeated root" for D=0.

 

[kreshnik]

"Double" here should mean the solutions are twins.


So, you need D = 0, so that there is a repeated solution.

$So, \ set \ \ 16 - 16a \ \ equal \ to \ 0 \ and \ solve$

$\ for \ that \ value \ of \ a.$


*** Edit


That means that a = 1.

So, the answer is B.



***2nd edit:

Curious3141 repeated the essence of what I already stated.

No, by double, I meant: example: $$x_1=3\;\;,\;\;x_2=7$$ just example, not twins or the same but two different, sorry for that.

Terrible question. "Double solutions" is nonsensical. It's either "distinct real roots" for D>0 or "single repeated root" for D=0.

"Terrible question??" let's see if you understand it in my Language.!

Sa duhet të jetë parametri a ashtuqë ekuacioni $$ax^2-4a+4=0$$ te kete dy zgjidhje te ndryshme?

Do you like that??... English is a FOREIGN language for me, and I'm not blaming you for anything, It's ok that you defined it "Terrible question" , but try to understand (ask me) before you judge! So I guess, C and D should be correct, am I wrong?

 

[Curious3141]

No, by double, I meant: example: $$x_1=3\;\;,\;\;x_2=7$$ just example, not twins or the same but two different, sorry for that.
"Terrible question??" let's see if you understand it in my Language.!

Sa duhet të jetë parametri a ashtuqë ekuacioni $$ax^2-4a+4=0$$ te kete dy zgjidhje te ndryshme?

Do you like that??... English is a FOREIGN language for me, and I'm not blaming you for anything, It's ok that you defined it "Terrible question" , but try to understand (ask me) before you judge! So I guess, C and D should be correct, am I wrong?

No need to get all grumpy. I was commenting on the question as it was phrased, and I naturally assumed that was how it had been presented to you. How was I supposed to know you had translated it in an ambiguous fashion? I am not a mindreader.

In any case, if you meant TWO separate real roots, there is no unique answer, as LearninDaMath has already pointed out to you. C and D both fit.

 

[sankalpmittal]

Homework Statement

How should be the value of a so quadratic equation $$ax^2-4x+4=0$$ to have double solutions?
$$A)\;\;2$$
$$B)\;\;1$$
$$C)\;-1$$
$$D)\;-2$$

Homework Equations

The Attempt at a Solution

$$D=b^2-4ac$$
If:
$$D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}$$
$$D=0\;\;\rightarrow\; {x_1}\;\rightarrow\;\text{only one solution}$$
$$D<0\;\;\rightarrow\; \text{no solution.}$$

so:
$$(-4)^2-4*a*4=16-16*a$$
$$\text{If:}\;\;a=-1\;\;\rightarrow\;D=32$$
$$\text{If:}\;\;a=-2\;\;\rightarrow\;D=48$$

Which one should be?? thank you.

Kreshnik , here double roots means "real and distinct roots."
Here discriminant is greater than 0.

D>0
You have

D=b²−4ac
or
b²−4ac > 0
Plug in the values and find for a i.e. inequality in "a".
What do you get ?

 

[ehild]

Sankaplmittal,

double roots mean that the roots are equal. http://www.tpub.com/math1/17g.htm
Kreshnik has shown already at what values of parameter "a" the discriminant is greater than zero, so the equation has two real and distinct roots .

ehild

 

[kreshnik]

No need to get all grumpy. I was commenting on the question as it was phrased, and I naturally assumed that was how it had been presented to you. How was I supposed to know you had translated it in an ambiguous fashion? I am not a mindreader.

In any case, if you meant TWO separate real roots, there is no unique answer, as LearninDaMath has already pointed out to you. C and D both fit.

Curious3141 I hope I didn't offend you, if I did it, I'm sorry.
Thanks everyone for being patience. I think now I learned what I wanted to know.
Thank you everyone.

 

[Curious3141]

Curious3141 I hope I didn't offend you, if I did it, I'm sorry.
Thanks everyone for being patience. I think now I learned what I wanted to know.
Thank you everyone.

No worries, didn't mean to offend you either, and glad you learned what you wanted to know.

 

[Mark44]

Sa duhet të jetë parametri a ashtuqë ekuacioni $$ax^2-4a+4=0$$ te kete dy zgjidhje te ndryshme?

Out of curiosity, what language is this? Hungarian?

 

[LearninDaMath]

No need to get all grumpy. I was commenting on the question as it was phrased, and I naturally assumed that was how it had been presented to you. How was I supposed to know you had translated it in an ambiguous fashion? I am not a mindreader.

In any case, if you meant TWO separate real roots, there is no unique answer, as LearninDaMath has already pointed out to you. C and D both fit.

I never encountered a problem where I had to choose a number that produced two identical roots. I've only had to show whether there were two real, two complex, or 1 roots. I saw this question and thought i'd try my best to be productive by contributing while patiently waiting for my most recent thread to garner a little help lol.

 

[SammyS]

I never encountered a problem where I had to choose a number that produced two identical roots. I've only had to show whether there were two real, two complex, or 1 roots. I saw this question and thought i'd try my best to be productive by contributing while patiently waiting for my most recent thread to garner a little help lol.

If you're referring to a quadratic equation, then the case of "1 roots" is the same as the case of two identical real roots .

 

[LearninDaMath]

If you're referring to a quadratic equation, then the case of "1 roots" is the same as the case of two identical real roots .

Oh, so asking for "double solutions" or "two identical solutions" is the same thing as asking for 1 solution? If so, then of course, makes sense. Is it common for the x that yields 1 root to be asked in the terminology of finding "two identical solutions?" I don't recall hearing it put like that before.

 

[ehild]

Out of curiosity, what language is this? Hungarian?

No, it is not.

But Google said it was Albanian, and "te kete dy zgjidhje te ndryshme" = "Have two different solutions"

Is it right, Kreshnik?

ehild

 

[kreshnik]

No, it is not.

But Google said it was Albanian, and "te kete dy zgjidhje te ndryshme" = "Have two different solutions"

Is it right, Kreshnik?

ehild

Exactly...I hope you're convinced now. I'm albanian, Kosova.
Cheers!

 

[Bacle2]

Mark44 wrote:

"Out of curiosity, what language is this? Hungarian? "

I think the value of the roots is the same in any language ;) .

 

[ehild]

Exactly...I hope you're convinced now. I'm albanian, Kosova.
Cheers!

So we live quite close -I am Hungarian.

ehild

 

[kreshnik]

So we live quite close -I am Hungarian.

ehild

I guess we do! I'm glad we're neighbour. Take care.