Question

. If α,β andγ are the zeroes of the polynomial 3x^3+5x^2-9x+3 then the value of 1/α+1/β+1/γ is

Answer 1

❍ Given that, α, β and γ are the zeroes of the polynomial 3x³ - 5x² -9x + 3.

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To calculate the 1/α + 1/β + 1/γ  we must know  that ::

• Sum of the zeroes of the quadratic equation -  

           α + β + γ  = -b/a

•  Products of the zeroes of the quadratic equation -

           αβγ  = - d/a

• Sum of products of αβ + βγ+ αγ zeroes -

          αβ + βγ+ αγ = c/a

Finding  1/α + 1/β + 1/γ   :-

⤳ 3x³ - 5x² -9x + 3

☀️ Here,

• a denotes 3
• b denotes - 5
• c denotes - 9
• d denotes 3

⤳ α + β + γ  = - ( - 5 )/3  = 5/3

⤳ αβγ  = -3/3 = -1

⤳ αβ + βγ+ αγ = -9/3 =  -3  

[  By above information ]

⤳ 1/α + 1/β + 1/γ  = αβ + βγ+ αγ/ αβγ  

~ By substituting the values we've got above.

⤳ -3/-1

⤳ 3

 

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• Henceforth, value of  1/α + 1/β + 1/γ   is 3.

Answer 2

Answer:

3

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