Question

If alpha and beta are the zeroes of the quadratic polynomials f (x)=6 square +x-2 find the value of alpha/beta,beta/alpha

Answer 1

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$<i>$
Given :

f ( x ) = 6x² + x - 2

By Middle Term Factorisation,

f ( x ) = 6x² + 4x - 3x - 2

f ( x ) = 2x ( 3x + 2 ) - 1 ( 3x + 2 )

f ( x ) = ( 2x - 1 ) ( 3x + 2 )

To find zeroes, f ( x ) = 0

•°•

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

( 2x - 1 ) = 0 And ( 3x + 2 ) = 0

x = 1 / 2 And x = - 2 / 3

Let,

Zeroes be $\alpha$ And $\beta .$

•°•

$\alpha$ = 1 / 2 And $\beta$ = - 2 / 3

Now,

( i ) $\alpha$ / $\beta$

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

= 1 / 2 × - 3 / 2

= - 3 / 4

( ii ) $\beta$ / $\alpha$

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

= - 2 / 3 × 2

= - 4 / 3

Hence,

$\alpha$ / $\beta$ = - 3 / 4

And

$\beta$ / $\alpha$ = - 4 / 3

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