Question

If\[\LARGE{\alpha,\beta}\]are roots of the equation (x-a)(x-b)+k=0 then a, b will be the roots of the equation?????
@apoorvk @Eyad @jhonyy9 @jlvm @Hero @AravindG @UnkleRhaukus Plz help:)

Answer 1

Sum of roots is given by : -B/A
Product of roots is given by : C/A

Answer 2

I think this question is poorly written by the textbook or instructor.

Answer 3

I believe it's asking if \((x-\alpha)(x-\beta)+k=0\), then, what must \(k=\)?
The answer is a bit obvious. Have you thought on this, TheViper?

Answer 4

Is there any typo?? @Limitless

Answer 5

Ques is fully right:)

Answer 6

I think it will be:

\[ab = k - \alpha \beta\]

Isn't it @apoorvk ??

Answer 7

@apoorvk, so, you think this is asking for an equation \(f(x)=0\) in terms of \(\alpha\) and \(\beta\)?

Answer 8

\[\Huge{\color{green}{\cal{Equation:-}}}\]\[\LARGE{\color{blue}{{(x-\alpha)(x-\beta)-k=0??}}}\]

Answer 9

@TheViper, do you intentionally mean a difference between a and \(\alpha\)? Likewise, b and \(\beta\) are different?

Answer 10

this is answer given in book:)

Answer 11

Oh yes I made an error there, thanks @waterineyes

So,
\(x^2−(a+b)x+(ab−k)=0\) has roots α and β.




Now sum of roots = -B/A = (a+b) = α + β ...{i}

Product of roots = αβ = ab - k
or, ab = k - αβ ...{ii}



Now a quadratic with roots 'a' and 'b' is \(x^2−(a+b)x+ab=0\)

Substitute the values of 'a+b' and 'ab' from {i} and {ii} respectively, and enjoy!

Answer 12

It is okay..

Answer 13

can i have the full sol @apoorvk I here also so confused:(

Answer 14

Yes @Limitless I agree that the language of the question is pretty misleading. :|

Answer 15

@TheViper you're just a step away from the answer, try to ho through this thing just once more pretty slowly, am sure you'll figure out what we're doing in here.

Answer 16

Just plug in the values of a+b and ab and you will have equation having roots a and b..

Answer 17

how can be sum of roots=-B/A @apoorvk

Answer 18

It is...

Answer 19

@TheViper am sorry I should have mentioned that:
Compared with a standard quadratic equation of the form \(Ax^2 + Bx + C =0\)

sum of roots = -B/A
and
product of roots = C/A


You must have heard of this I believe?

Answer 20

no

Answer 21

No? Umm, what grade are you in currently?

Answer 22

oh I see it with more concentration I know it:)
Product of roots=constant term/co-efficient of x^2
Sum of rots=-co-efficient of x/co-efficient of x^2

Answer 23

Yes Sire! Now you get it! :)

Hmm so does it seem to make any sense now?

Answer 24

k thanx all of u now I can do it:)

Answer 25

yes

Answer 26

thanx @waterineyes @apoorvk :)

Answer 27

You're welcome!

Answer 28

Welcome dear..