Question

The quadratic equation whose root are in A.M and H.M is equal to the sum of squares of their reciprocals, 2x^2-3x+5=0 is
(A) 4x^2-3x+5=0
(B)12x^2-49x+30=0
(C)14x^2-12x+35=0
(D)2x^2+3x+5= 0

Answer 1

@dan815 pls help

Answer 2

@luigi0210 pls save my life

Answer 3

@hartnn pls help

Answer 4

i am not clear with the question...whose roots are in AM?

Answer 5

i will rewrite the question

Answer 6

The quadratic equation whose roots are the AM and HM between the roots of the equation 2x^2-3x+5=0

Answer 7

is- and option are the same

Answer 8

better.

Answer 9

i am sorry

Answer 10

a bit tensed

Answer 11

no problem. :)
so,
2x^2-3x+5=0

can you find sum of roots and product of roots of this quadratic ?

Answer 12

yes

Answer 13

AM means arithmetic mean.
AM of 2 numbers will be sum of those 2 numbers divided by 2

so what will be the AM ?

Answer 14

wait for a minute

Answer 15

but there are no real roots for this equation

Answer 16

you can still find the sum of roots.

have you ever head that
sum if roots for \(ax^2+bx+c\) would be \(\Large \dfrac{-b}{a}\)
?

Answer 17

no

Answer 18

ok

Answer 19

so 3/2

Answer 20

correct.

Answer 21

now product of roots,
for ax^2 +bx+c,
product of roots is just c/a

Answer 22

ok

Answer 23

yes i have heard

Answer 24

5/4

Answer 25

alpha+beta=-b/a
alpha+beta=c/a

Answer 26

thats correct!

so, AM = sum/2 = 3/4

Answer 27

know what HM is ?

Answer 28

sqrtab

Answer 29

no, thats geometric mean :)

Answer 30

ohhh sorry

Answer 31

1/HM = 1/a + 1/b

Answer 32

yes

Answer 33

so HM = ab/ (a+b)

Answer 34

ab = product = 5/2
a+b = sum = 3/2
find HM now

Answer 35

(a+b/n)^-1

Answer 36

5/3

Answer 37

yep,
HM = 5/3

so now you have both roots
3/4 and 5/3
can you make an equation ?

Answer 38

yes

Answer 39

so sorry i asked such a silly question

Answer 40

i wasn't silly. it was a good question :)
and even silly questions are welcome here, there's always something to learn from silly questions too :)

Answer 41

**it wasn't silly

Answer 42

thnx

Answer 43

i read it gm

Answer 44

welcome ^_^