If α, β are the roots of x² - 5x + k = 0, find k such that 3α + 2β = 16?
- 4
- 3
- -6
- None of these
Explanation
Given:
α + β = 5 (sum of roots)
αβ = k (product of roots)
3α + 2β = 16
From α + β = 5, we get:
α = 5 - β
Substitute α in 3α + 2β = 16:
3(5 - β) + 2β = 16
15 - 3β + 2β = 16
-β = 1
β = -1
Now, α = 5 - β
α = 5 - (-1)
α = 6
k = αβ
k = 6 × (-1)
k = -6
Related MCQs
- Commutative
- Associative
- Distributive
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- 233
- 133
- 333
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
