If α and β are the zeroes of the quadratic polynomial f(x)= x²-5x+4, then the value of 1/α+1/β-2αβ is?
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Answers
Answered by
6
Hey mate! here is your answer!!!
α and β are the zeroes of the polynomial f(x).
By co-efficient and zeroes relations, we get
Sum of Zeroes = α+β = -b/a = -(-5)/4 = 5/4
Product of Zeroes =αβ = c/a = 4/1 = 4
1/α+1/β - 2αβ
= β- 2αβ/α + 1
= β-2×4/α + 1
=β-8/α+14
=1-8/ 4+14
=(-9)/18
=(-1)/2
hope it helped!!!
α and β are the zeroes of the polynomial f(x).
By co-efficient and zeroes relations, we get
Sum of Zeroes = α+β = -b/a = -(-5)/4 = 5/4
Product of Zeroes =αβ = c/a = 4/1 = 4
1/α+1/β - 2αβ
= β- 2αβ/α + 1
= β-2×4/α + 1
=β-8/α+14
=1-8/ 4+14
=(-9)/18
=(-1)/2
hope it helped!!!
TechnoSwayam:
waot
Answer is -27/4 :?
no bro
check it. I find the values of
α and β by factorisation of polynomial
I have the answer key bro
but not have the method :(
Answered by
13
Heya !!!
F(X) = X² -5X+4
Here,
A = 1 , B = -5 and C = 4
Sum of zeroes = -B/A
Alpha + Beta = 5 -------(1)
And,
Product of zeroes = C/A
Alpha × Beta = 4 --------(2)
Therefore,
1/Alpha + 1/Beta - 2 Alpha × Beta
Beta + alpha / Alpha×Beta - 2Alpha × Beta
=> 5/ 4 - 2 ×4
=> 5/4 - 8
=> 5-32/4
=> -27/4
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
F(X) = X² -5X+4
Here,
A = 1 , B = -5 and C = 4
Sum of zeroes = -B/A
Alpha + Beta = 5 -------(1)
And,
Product of zeroes = C/A
Alpha × Beta = 4 --------(2)
Therefore,
1/Alpha + 1/Beta - 2 Alpha × Beta
Beta + alpha / Alpha×Beta - 2Alpha × Beta
=> 5/ 4 - 2 ×4
=> 5/4 - 8
=> 5-32/4
=> -27/4
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
oh!The question was so;However I havent think of it
just needed to To do is to Get LCM of Alpha and beta :(
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