Question

if alpha and beta are zeros of the polynomial p(x)=3x^2-5x+6 find alpha/beta+beta/alpha

Answer 1

$\textbf{- Answer -}$

Here, the polynomial is

p (x) = 3x² - 5x + 6

Since, α and β are the zeros of p (x),

α + β = - (- 5)/3

⇒ α + β = 5/3 ...(i)

and

αβ = 6/3

⇒ αβ = 2 ...(ii)

Now, α/β + β/α

= (α² + β²)/(αβ)

= {(α + β)² - 2αβ}/(αβ)

= {(5/3)² - (2 × 2)}/(2)

= (25/9 - 4)/2

= (25 - 36)/(4 × 2)

= - 11/8

#$\textbf{MarkAsBrainliest}$

Answer 2

Heya !!!

P(X) = 3X²-5X+6

Here,

A = 3 , B = -5 and C = 6

Sum of zeroes = -B/A

Alpha + Beta = -(-5) / 3

Alpha + Beta = 5/3 -----(1)

And,

Product of zeroes = C/A

Alpha × Beta = 6/3

Alpha × Beta = 2 ------(2)

Therefore,

Alpha / Beta + Beta/ Alpha

=> { ( Alpha)² + (Beta)² }/ Alpha × Beta

=> { ( Alpha+Beta )² - 2 Alpha × Beta } / Alpha × Beta

=> ( 5/3)² - 2 × 2 / 2

=> 25 /9 - 4 /2

=> 25 - 36 /9 /2

=> -11 /9 / 2

=> -11 /9 × 1/2

=> -11/18



HOPE IT WILL HELP YOU.... :-)