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Question

If both the roots of the equation x232x+c=0 are prime numbers then the possible values of c are

A
60
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B
87
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C
247
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D
231
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Solution

The correct options are
B 87
C 247
The roots of x232x+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 3×29=87 and 13×19=247.

Hence c=87 and 247


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