Premise1: Potato cyst nematodes are a pest of potato crops.
Premise2: The nematodes can lie dormant for several years in their cysts, which are protective capsules, and
Premise3: The Nematodes do not emerge except in the presence of chemicals emitted by potato roots.
Premise4: A company that has identified the relevant chemicals in planning to market them to potato farmers to spread on their fields when no potatoes are planted;
Conclusion: any nematodes that emerge will soon starve to death.
(A) Nematodes that have emerged from their cysts can be killed by ordinary pesticides.
This is against conclusion, which says nematodes will die because of starvation. So even if nematodes can be killed by pesticides but this is not strengthening the passage.
(B) The only part of a potato plant that a nematode eats is the roots.
Premise3 implies tells that roots release certain chemicals that make nematodes active. Premise 4 tells company has developed similar chemical and it needs to be spread while there is no potatoes in the field. As this sentence implies if nematodes only eats roots of potato plant. But as this company produced chemical make nematodes active and when they found nothing to eat as potato fields are not ready. So chemical is tricking nematodes. This strengthen the case successfully. Note that this sentence is joining two premises as well as focusing on conclusion so strongest contender.
(C) Some bacteria commonly present in the roots of potatoes digest the chemicals that cause the nematodes to emerge from their cysts.
If at all this will weaken the case. Because bacteria is also present when potatoes are there in the field.
(D) Trials have shown that spreading even minute quantities of the chemicals on potato fields caused nine-tenths of the nematodes present to emerge from their cysts.
This is good alternative that tells that 90% of nematodes will come out. But do they die because of starvation how is this strengthening the conclusion.
(E) the chemicals that cause the nematodes to emerge from their cysts are not emitted all the time the potato plant is growing.
Premise4 says that chemical is spread only when there is no potatoes in field, so this option is irrelevant.