Question

If the quadratic equation ax^2-2bx+c=0 has two equal roots, which of the following is / are true?
A. a,b,c form an arithmetic progression.
B. a,b,c form a geometric progression.
C. Both roots are b/a

Answer 1

@ganeshie8

Answer 2

say, the common root is k

Answer 3

k+k = ?
k*k = ?

Answer 4

u familiar with the sum of roots, product of roots ?

Answer 5

sum of roots = -b/a
product of roots = c/a

Answer 6

OMG, i am weak in sum of roots..

Answer 7

its okay, use those, and find
k+k = ?

Answer 8

why 2 common roots?

Answer 9

yea,

ax^2-2bx+c=0

sum of roots k+k = --2b/a
2k = 2b/a
k = b/a -----------------(1)

Answer 10

product of roots k*k = c/a
k^2 = c/a --------------(2)

Answer 11

a, b, c
a, ak, ak^2 ( using (1) and (2) )

Answer 12

so, a, b, c are in geometric progression with a common ratio of k

Answer 13

see if that makes some sense

Answer 14

oh, i understand now. a,b,c cannot form an arithmetic progression?

Answer 15

they cant, cuz there is no common difference

Answer 16

there is oly a common ratio, so GP

Answer 17

I would use an easier method. two roots are equation=determinant is 0, that is, b^2-4ac=0,thus, ac=(b/2)^2,which leads to the conclusion that a,b,c form a GP

Answer 18

sorry two roots are equal, not two roots are equation. Typo is frustrating!

Answer 19

okay, clear.
i want to ask is there any numbers can both form an arithmetic progression and GP.?

Answer 20

let me see, if three numbers are a,b,c then b^2=ac and a+c=2b, is that possible, I don't know!

Answer 21

okay, thanks:)

Answer 22

wait a minute! (2b)^2=4ac so a+c)^2=4ac so a-c)^2=0 so a=c but a has to be greater than c to form a meaningful AP, so NO, the series does not exist!