Question
From the set of first 10 natural numbers, three distinct prime numbers a, b and c are selected to form a quadratic equation ax2 + bx + c = 0, having real roots. Find the sum of the roots of all such possible quadratic equations that can be formed.
Answer: Option E
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E
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E
The two real roots of each of the possible quadratic equations will be distinct. For real roots we must have b2 ≥ 4ac. As a, b and c distinct prime numbers from 1 to 10, only the following triplets (a, b, c) are possible: (2, 5, 3), (3, 5, 2), (2, 7, 3), (3, 7, 2), (2, 7, 5), (5, 7, 2).
Accordingly, the sum of roots of all such formed is
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