Question

if alpha and beta are the zeros of the quadratic polynomial 6xsquare + x - 2 find the value of Alpha upon beta + beta upon Alpha

Answer 1

$\textbf{ - Answer}$

The given polynomial is

f (x) = 6x² + x - 2

Since α and β are the zeros of f (x),

α + β = - 1/6 ...(i)

and

αβ = (- 2)/6

⇒ αβ = - 1/3 ...(ii)

Now, α/β + β/α

= (α² + β²)/(αβ)

= {(α + β)² - 2αβ}/(αβ)

= {(- 1/6)² - 2 (- 1/3)}/(- 1/3)

= (1/36 + 2/3)/(- 1/3)

= {(1 + 24)/36}/(- 1/3)

= (25/36)/(- 1/3)

= - 25/36 × 3

= - 25/12

#$\textbf{MarkAsBrainliest}$

Answer 2

Heya !!!

P(X) = 6X²+X-2

Here,

A = 6 , B = 1 and C = -2

Sum of zeroes = -B/A

Alpha + Beta = - 1 / 6 ------(1)

and,

Product of zeroes = C/A

Alpha × Beta = -2/ 6 = -1/3 -------(2)

Therefore,

Alpha / Beta + Beta / Alpha

=> (Alpha)² + (Beta)² / Alpha × Beta

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

=> ( -1/6)² - 2 × -1 / 3 / -1/3

=> 1 / 36 + 2 /3 / -1 /3

=> 1 +24 / 36 / -1 /3

=> 25 / 36 / -1 /3

=> 25 / 36 × 3/ -1

=> 25 / -12


=> -25/12



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