Question

From the set of first 10 natural numbers, three distinct prime numbers a, b and c are selected to form a quadratic equation $a{x}^2+bx+c=0$, having real roots. Find the sum of the roots of all such possible quadratic equations that can be formed.

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

Answer 1

The correct option is D -149/10

The two real roots of each of the possible quadratic equations will be distinct. For real roots we must have $b^2\ge 4ac$. 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

$=\frac{-5}{2}+\frac{-5}{3}+\frac{-7}{2}+\frac{-7}{3}+\frac{-7}{2}+\frac{-7}{5}=\frac{-149}{10}$