Question

if alpha and beta are the zeros of x square + 5 x + 6 find the value of Alpha power -1 and beta power -1​

Answer 1

Given:

—————–

=> polynomial : x²+5x+6

=> zeroes of the polynomial : α and β

Prove:

—————

=> α‐¹ and b‐¹

Solution:

————————

by factoring,

=> x²+5x+6 = 0

=> x²+2x+3x+6 = 0

=> x ( x+2 ) + 3 ( x+2 ) = 0

=> ( x+3 ) ( x+2 ) = 0

=> x + 3 = 0 | => x + 2 = 0

=> x = - 3 | => x = - 2

therefore,

=> α = - 3 | => β = - 2

By the problem,

we have to find α‐¹ and b‐¹

=> α‐¹ = ( -3 )‐¹ | => b‐¹ = ( -2 ) ‐¹

= 1 / -3 | => = 1 / -2

therefore,

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[ α‐¹ = 1 / -2 ] and [ b‐¹ = 1 / -2 ]

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