Question

If both the roots of the equation $x^2-32x+c=0$ are prime numbers then the possible values of $c$ are

• A. $60$
• B. $87$
• C. $247$
• D. $231$

Answer 1

Answer: (B), (C)

The correct options are
B $87$
C $247$

The roots of $x^2-32x+c=0$ are prime numbers.

Let $x,y$ be the prime roots.

Here $x+y=32$

Ordered pair $(x,y)$ satisfying this are

• $(0,32)$
• $(1,31)$
• $(2,30)$
• ...
• $(16,16)$

Now the only pairs containing both prime numbers are

$(x,y)=(3,29)and(13,19)$

Here $c$ is product of roots.

Therefore possible values of $c$ are $3\times 29=87$ and $13\times 19=247$.

Hence $c=87$ and $247$