Question

if alpha and beta are the zeroes of polynomial 6x^2+x-1 then find the value of alfa upon beta plus beta upon alpha

Answer 1

6x²+x-1=0

6x²+3x-2x-1=0
3x(2x+1)-1(2x-1)=0
(3x-1)(2x-1)=0

x=1/2,1/3

Alpha =1/2
Beta=1/3

Alpha/beta+beta/ Alpha= 1/2/1/3+ 1/3/1/2
= 3/2+2/3
= 9+4/6
= 13/6
= 2 1/6

Answer 2

$\bold {\huge{Ello!!}}$

$<b >Here's your answer$

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Given polynomial , 6x² + x - 1 = 0 -------- ( i )

And it's zeros α and β

To find the value of : α / β + β / α

Equation no ( i ) is Compared with ap² + bp + c = 0

Then we get ,

a = 6

b = 1

c = - 1

Now ,

Sum of the zeros , ( α + β ) = - b / a

= - ( 1 ) / 6

= - 1 / 6

And , Product of the zeros , ( α × β ) = c / a

= - 1 / 6

Now ,

α² + β²

= ( α + β )² - 2αβ

= ( - 1 / 6 )² - 2 × ( - 1 / 6 ) [ • Putting the values ]

= 1 / 36 + 1 / 3

= 1 + 12 / 36

= 13 / 36

Thus ,

α / β + β / α

= α² + β² / αβ

= ( 13 / 36 ) / ( - 1 / 6 ) [ • Putting the values ]

= - 13 / 36 × 6 / 1

= - 13 / 6 [ ★ Required answer ]

So , the value of the following is - 13 / 6.

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$<b><u><marquee direction> Hope it helps !!$