if alpha and beta are the zeros of the quadratic polynomial 3x^2-4x+1 find a quadratic polynomial whose zeros are alpha^2/beta and beta^2/alpha. someone please answer.
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p(x)= 3x² - 4x +1 = 0
let's roots be a and b
sum of roots = a + b = 4/3
product of roots = 1/3
now for new one roots are , a²/b and b²/a
sum of roots = a²/b + b²/a = a³ + b³ / ab =
⇒ (a+b)(a² + b² - ab )/ ab = (a+b)[(a+b)² - 2ab -ab]/ab
= 28/9
product of roots = a²/b * b²/a = ab = 1/3
now new equation gonna be ⇒ x² - 28/9x + 1/3 ⇒ 9x² -28x +3 =0
hope so I'm right ..........if any queries then ask
let's roots be a and b
sum of roots = a + b = 4/3
product of roots = 1/3
now for new one roots are , a²/b and b²/a
sum of roots = a²/b + b²/a = a³ + b³ / ab =
⇒ (a+b)(a² + b² - ab )/ ab = (a+b)[(a+b)² - 2ab -ab]/ab
= 28/9
product of roots = a²/b * b²/a = ab = 1/3
now new equation gonna be ⇒ x² - 28/9x + 1/3 ⇒ 9x² -28x +3 =0
hope so I'm right ..........if any queries then ask
siddharthverma1:
hey watch carefully there is square sign on 3x
maybe i should send u a pic then u will understand it
nope u don't need to send anything ....actually i accidentally added my ans...i haven't completed it ...i'm still answering .......... so wait
oh i thought so
hehe thanks .i just wanted to check my answer.
tell me something what if we dont multiply 9 in the end then will our answer be incorrect
nope ...we do take lcm for convenience......or say equation looks good
oh thanks a lot
ur welcome
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