Question

equation x^2+2x+3=0 roots are x1 and x2. the quadratic equation with the roots 1/x1 and 1/x2 is
A. 3x^2+2x-1=0
B. 3x^2+2x+1=0
C. 3x^2 -2x+1=0
D. x^2-2x+3=0
E. x^2-2x-3=0

Answer 1

Is you remember the formula I used in previous question:

If u and v are the roots of a quadratic equation ax^2 + bx + c = 0, then,

\[\large{u+v = \cfrac{-b}{a}}\]

\[\large{uv = \cfrac{c}{a}}\]

Answer 2

Now, here the roots of the equation x^2 + 2x + 3 = 0 are x1 and x2.

So, can you calculate x1 + x2 and x1 * x2 ?

Answer 3

@dinisha you there ?

Answer 4

ya i am trying to solve

Answer 5

Ok take your time :)

Answer 6

u+v=-2/1=-2
uv=3/1=3
x1+x2=-2
x1*x2=3

Answer 7

Very good

Answer 8

Now, you have been asked to find an equation with roots 1/x1 and 1/x2.

Okay let the equation be : ax^2 + bx + c = 0

Now, you know that this equation has roots 1/x1 and 1/x2.

(1) Find out 1/x1 + 1/x2 and 1/x1 * 1/x2 using the values of x1 + x2 and x1*x2.

(2) Find out 1/x1 + 1/x2 and 1/x1 * 1/x2 in terms of a, b and c.

Answer 9

in that case if 1/x1+1/x2 will it be -1/2 and 1/x1*1/x2=1/3 ???

Answer 10

1/x1 * 1/x2 is correct. But, (1/x1) + (1/x2) is not. See:

\[\large{\cfrac{1}{x_1} + \cfrac{1}{x_2} = \cfrac{x_1+x_2}{x_1\times x_2}}\]

Answer 11

Now, you already know the values of x1 + x2 and x1*x2.

Answer 12

@dinisha ?

Answer 13

is it -2/3 ??? @vishweshshrimali5

Answer 14

Yes

Answer 15

Now tell me what is 1/x1 + 1/x2 and 1/x1 * 1/x2 in terms of a,b and c.

Answer 16

wait a minute i am trying now!!

Answer 17

take your time :)

Answer 18

1/x1+1/x2 = -a/b
1/x1*1/x2 = -b/c

Answer 19

Nope

Answer 20

Some of roots (for ax^2 + bx + c = 0) = -b/a

Product of roots = c/a

Answer 21

a=1, b=-2, c=3
ax^2+bx+c=0
x^2-2x+3=0
Am I right?

Answer 22

Hey hey slow down...

First of all how did you obtain a,b, and c ?

Second thing that's wrong.

Answer 23

whr did i went wrong??

Answer 24

First of all tell me how did you find out a, b, and c ?

Answer 25

\(\color{blue}{\text{Originally Posted by}}\) @vishweshshrimali5
Some of roots (for ax^2 + bx + c = 0) = -b/a

Product of roots = c/a
\(\color{blue}{\text{End of Quote}}\)

Thus, 1/x1 + 1/x2 = -b/a

and 1/x1 * 1/x2 = c/a

Answer 26

yaa soo wat i did was i compared the equation with terms and the answer i got for 1/x1+1/x2 and 1/x2*1/x2

Answer 27

Okay lets see:

1/x1 + 1/x2 = -2/3 = -b/a

1/x1 * 1/x2 = 1/3 = c/a

So, a = 3, b= 2, c = 1

So, ax^2 + bx + c = 0

=> 3x^2 + 2x + 1 = 0

Answer 28

Did you get your mistake ?

Answer 29

@dinisha ??

Answer 30

yaaa i got it!! thank u :) @vishweshshrimali5

Answer 31

np :)