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.

• A. -19/2
• B. 38
• C. -27/5
• D. - 87/10
• E. -149/10

Answer 1

The correct option is D - 87/10

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