if alpha and beta are zeroes of polynomial 6x2+x-1,then find the value of
1.alpha cube beta+alpha beta cube
2.alpha/beta+beta/alpha+2(1/alpha+1/beta)+3alpha beta
Answers
Answer: i) -13/216
ii) -2/3
Step-by-step explanation:
p(x) = 6x²+x-1
Let the zeroes be α & β
α+β = -coefficient of x ÷ coefficient of x² = -1/6
αβ = constant term ÷ coefficient of x² = -1/6
1} α³β+αβ³ = αβ (α²+β²)
= αβ { (α+β)²- 2αβ }
on putting the values ,
=-1/6 { (-1/6)² -2×(-1/6)}
=-1/6 { 1/36 + 2/6 }
= -1/6 (13/36)
= -13/36 ...... Ans
2) α/β + β/α +2{1/α + 1/β } +3αβ
=(α²+β²)/αβ + 2 { (α+β)/αβ } + 3αβ
on putting the values.....
= {(-1/6)²- 2(-1/6)} / -1/6 + 2 {(-1/6)/(-1/6)} +3×(-1/6)
= -13/6 + 2 - 1/2
= (-13 +12 - 3) / 6
= -4/6
= -2/3 .................. Ans
PLEASE MARK IT BRAINLIEST .......
Step-by-step explanation:
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