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The value of k for which the roots α, β of the equation : x2 − 6x + k = 0 satisfy the relation 3α + 2β = 20, is
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- 8
- - 8
- 16
- - 16
Correct Option: A
According to question , we have
The roots α, β of the equation : x2 − 6x + k = 0
On comparing with ax2 + bx + c = 0 , we get a = 1 , b = - 6 , c = k
Now , α + β = ( - b/a ) = 6
α + β = 6 and 3α + 2β = 20
On solving ,
⇒ α = 4, β = 2
Product of the roots = k
So, k = αβ = 4 × 2 = 8.
Hence , required answer will be option A .
