Question
If x3−k2x2+(6k+5)x−5k=0 has two roots 3 and 5, then which of the following is the third root?
Answer: Option A
:
A
Assumeαbe the 3rd root.
Sum of the roots, i.e.,3+5+α=k2
Product of the roots, i.e.3×5×α=5k
So,8+α=9α2
Then,α=1or−89
Hence the 3rd root is 1.
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:
A
Assumeαbe the 3rd root.
Sum of the roots, i.e.,3+5+α=k2
Product of the roots, i.e.3×5×α=5k
So,8+α=9α2
Then,α=1or−89
Hence the 3rd root is 1.
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