Question

Find roots if two roots are equal :
4x^3+20x^2-23x+6=0

Answer 1

pls use the relation:
Roots: p,q,r
p+q+r= -b/a
pq+qr+pr= c/a
pqr = d/a

Answer 2

If two roots are equal then:

\[2p + r = -5\]

\[\large p^2r = \frac{3}{2}\]

Using these two equation find p and r..
Can you do it??

Answer 3

no

Answer 4

full sol. pls

Answer 5

as p=q, p+q=2p
nw 2p +r=-5------1)
nd p^2r=3/2------2)
frm 1) r=-5-2p-----3)
substitute 3)in 1)

Answer 6

den u'll get p^2(-5-2p)

Answer 7

we cant substitute 3) in 1)

Answer 8

=3/2

Answer 9

ya itz upto u

Answer 10

wait wait i dnt think u can do dat

Answer 11

lyk u get a value frm one equation nd hw can u substitute it in de same thing?

Answer 12

yes thats what i was saying

Answer 13

i mean 3) in 2)

Answer 14

well i got de equation no: wrong bt wat i did was ryt

Answer 15

den u can solve de quadraitic equation

Answer 16

the full sol. !

Answer 17

can u tell me de value of p? lyk i'm already workin on sme problemz

Answer 18

you mean the ans.?

Answer 19

solve fr p...p^2(-5-2p)=3/2

Answer 20

p is root we have to find p q and r..

Answer 21

if v get p, den (x-(p)) is a factor of the givn polynomial den v can divide de polynomila by (x-(p)) to get a quadratic polynimial den by splitting de middle term v get q nd r

Answer 22

i don't want the ans. from synthetic division.

Answer 23

bt v hav used de co efficient- zero relation ryt nd den only v r dividing...well dis is all i hav learnt

Answer 24

i guess u hav to bump de question to get de ans: srry

Answer 25

thanks

Answer 26

:)

Answer 27

@ganeshie8 @mukushla @nitz Does any one of you knows Theory of Equations?

Answer 28

do u mean proof of quadratic formula???

Answer 29

no

Answer 30

then wht???

Answer 31

google it.

Answer 32

http://en.wikipedia.org/wiki/Quadratic_equation

Answer 33

ok see this
Let's Suppose p=q
form
p+q+r= -b/a
pq+qr+pr= c/a
u have

2p+r=-5 -------->4p+2r=-10 -------->p+2r=-10-3p (I)
p^2+2pr=-23/4-------->p(p+2r)=-23/4 (II)

plug equation (I) in equation (II)
u will get

p(10+3p)=23/4 its a simple quadratic equation and it gives p=1/2 and p=-23/6

Answer 34

roots : 1/2, 1/2 , -6

Answer 35

Yeah I got it...

Answer 36

@shubham.bagrecha
p=1/2 and r=-5-2p=-6

Answer 37

ok

Answer 38

@mukushla why p=q=-23/6 and c=8/3 not taken??

Answer 39

when p=1/2,c=-6
when p= -23/6, c=8/3
??

Answer 40

check it with p^2 r=3/2

Answer 41

ok

Answer 42

got that

Answer 43

K