Question

pls solve all parts in detail


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Answer 1

Given Polynomial:

x² - x - 6

Factorizing the given Polynomial :-

x² - x - 6 = 0

So, by splitting the middle term method , We get

=> x² - 3x + 2x - 6 = 0

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

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

Here , x + 2 = 0

=> x = -2

also ,

x - 3 = 0

x = 3

Hence , it's two of the zeros are -2 and 3

and according to the question alpha and beta are the zeros of this Polynomial

So , alpha = -2

and

beta = 3

So ,

i) alpha² x beta + alpha x beta²

=> (-2)² x 3 + ( -2 x (3)² )

=> 4 x 3 + ( -2 x 9 )

=> 12 - 18 => -6

ii) alpha² + beta² - 2.alpha.beta

=> (-2)² + (3)² - 2 x -2 x 3

=> 4 + 9 + 12 => 25

iii) alpha - beta

=> -2 -3 => -5

iv) alpha²/beta + beta²/alpha

=> (-2)²/3 + (3)²/-2

=> 4/3 - 9/2

=> (8 - 27)/6

=> -19/6

This is the full step by step Explanation

Hope it helped you...