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What is the sum of the irrational roots of the equation (x-1)(x-3)(x-5)(x-7)=9 ?
a) 10
b) 8
c) 6
d) 4
Read Solution (Total 3)
-
- Given that
(x - 1) (x - 3) (x - 5) (x - 7) = 9
Let x - 4 = p
Then the given eqn becomes
(p + 3) (p + 1) (p - 1) (p - 3) = 9
(p2 - 1) (p2 - 9) = 9
p4 - 10p2 + 9 = 9
p2 (p2 - 10) = 0
p2 =0 or p2-10 =0
p = 0 or p = sqrt(10) or p = - sqrt(10)
then x - 4 = 0, x - 4 = sqrt(10) or x - 4 = - sqrt(10)
Now the roots of the given eqn are 4,4 + sqrt(10) and 4 - sqrt(10)
The irrational roots are 4+sqrt(10) and 4 - sqrt(10)
The sum of the irrational roots = 4 + sqrt(10) + 4 - sqrt(10) = 8.
Hence the answer is 8. - 8 years agoHelpfull: Yes(23) No(3)
- (4-1)(4-3)(4-5)4-7)=9
- 8 years agoHelpfull: Yes(9) No(7)
- how did you get 4 in the solution
- 8 years agoHelpfull: Yes(9) No(0)
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