Question

Let p and q be primes. The equation x^4 - px^3+q = 0 has an integer root. Find the sum of p and q.

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Consider 2 and 3 as they are smallest possible prime numbers (2 being the smallest).

Hence Case I

Let p=3 and q=2

x  

2

−3x+2=0 implies

(x−2)(x−1)=0

x=2 and x=1.

The roots are positive.

Therefore 1,2 can be possible roots.

Case II

p=2 and q=3

x  

2

−2x+3=0

B  

2

−4AC

=4−12

=−8

Now D<0.

Hence no real roots.

Therefore possible solutions are 1,2.