Question

if alpha and beta are the zeros of the quadratic polynomial x square - x - 4 find the value of 1 /Alpha +1/ beta-alpha*beta

Answer 1

$\textbf{- Answer -}$

The given polynomial is

f (x) = x² - x - 4

Since α and β are the zeros of f (x),

α + β = - (- 1)/1

⇒ α +β = 1 ...(i)

and

αβ = - 4/1

⇒ αβ = - 4 ...(ii)

Now,

1/α + 1/β - αβ

= (α + β)/(αβ) - (αβ)

= 1/(- 4) - (- 4)

= - 1/4 + 4

= (- 1 + 16)/4

= 15/4

#$\textbf{MarkAsBrainliest}$

Answer 2

Heya !!!




P(X) = X²-X-4


This equation is of the form of AX²+BX+C =0


Where,



A = 1 , B = -1 and C = -4



Sum of zeroes = -B/A



Alpha + Beta = -(-1)/1


Alpha + Beta = 1


And,



Product of zeroes = C/A


Alpha × Beta = -4/1



Alpha × Beta = -4




Therefore,



1/ Alpha + 1/ Beta - Alpha × Beta



=> Beta + Alpha / Alpha × Beta - Alpha × Beta


=> 1/ -4 - (-4)



=> 1 / -4 + 4


=> 1 + (-16)/-4



=> 1 -16/-4


=> -15/-4



=> 15/4





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