Question

Find a quadratic equation whose roots are the reciprocals of the roots of 3x^2+5x-2=0.

Answer 1

A + B = -5/3 where A and B are the roots of this equation
AB = 2/3

1/A + 1/B = (A + B) / AB
= -5/3 / 2/3
= -5/2
thats part of
now we need the va;ue of 1/A x 1/B

Answer 2

Roots of the given equation are -2 and 1/3
3x^2+5x-2=0.
3x^2 + 6x -x -2 =0
3x(x+2) - 1(x+2) = 0
3x-1) (x+2) = 0
x = 1/3 or -2

Now the reciprocals are 3 and -1/2
To find the equation we use the formula
x^2 - S x + P = 0
Where S is the sum of roots ( = 3 + (-1/2)) and P is product of roots which is -3/2
Get your answer!

Answer 3

this equals 1 / AB = 3/2
equation is

2x^2 - 5x + 3 = 0

Answer 4

which is right?

Answer 5

the rules i used
are for

ax^2 + bx + c = 0

if A and B are the roots
then A + B = -b/a
and AB = c/a

i havent checked them yet - i might have made a typo of course.

Answer 6

thank you

Answer 7

yes i have made a mistake sorry
AB should be -2/3
check second line of my first post - sorry

Answer 8

the method is correct though

Answer 9

is Lfcmaniac correct?

Answer 10

i'm checking now

Answer 11

yes the answer is
2x^2 - 5x -3 = 0
whose roots are 3 and -0.5

Answer 12

ok :)

Answer 13

we got there in the end!

Answer 14

how did he get this
3x^2 + 6x -x -2 =0

Answer 15

jimmyrep

Answer 16

ok - he multiplied the 3x (from 3x^2) by 2 (from -2) to get the 6x.Now the middle term is +5x so he took wrote - x (to get the +5x). he was aiming for +5x. If the middle term was -5x, he would have written -6x + x.

Answer 17

if the quadratic will factor his was the easiest way of solving this problem. My way was more general and can be used for quadratics that will not factor.

Answer 18

@jimmyrep, your method should always work, i just proved it from the quadratic formula.

Answer 19

mine was not the only quadratic that fits the bill in this problem
-5x^2 + 5x + 3 = 0 would also be an answer
so would
10x^2 - 10x - 6 = 0
but the question asked for 'a quadratic' so there are many answers

Answer 20

ty mike0