Question

if alpha and bita are the zeros ofquadraticpolynomial x2-5x+6 findthevalueof 1/alpha+ 1/
bita- 2alpha bita​

Answer 1

Answer:

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Answer 2

$\boxed{\textbf{\large{Step-by-step explanation:}}}$

▶Given quadratic polynomial is x² - 5x + 6

→ x² - 5x + 6 = 0

→ x - 3x - 2x + 6 = 0

→ x ( x - 3 ) - 2 ( x - 3 ) = 0

→ ( x - 2 ) ( x - 3 )

→ x = 2 OR x = 3

▶here the roots of quadratic equation are α and β

∴ α = 2 and β = 3

▶∴ we have to find out ,( (1 /α ) + ( 1/β )) - 2( α x β )

→ ( (1 /α ) + ( 1/β )) - 2( α x β )

= ( ( α + β ) /( α x β ))- 2 ( α x β )

[ ∴ α + β = 2 + 3 = 5 ]

[ ∴ α x β = 2 x 3 = 6 ]

= ( 5 / 6 ) - 2 ( 6 )

= ( 5 / 6 ) - 12

= ( 5 - 72 ) / 6.

= - 67 / 6

Therefor,

( (1 /α ) + ( 1/β )) - 2( α x β )

= - 67 / 6