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A quadratic equation with integral coafficients has two prime numbers as its roots. if the sum of the coefficients of the equation is prime then the sum of the roots is ?

A quadratic equation with integral coafficients has two prime numbers as its roots. if the sum of the coefficients of the equation is prime then the sum of the roots is ? 

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
12 years ago

Dear kamlesh

let equation is

ax2 +bx+c=0   and root are x1 and x2 and a,b,c are integer


x1 +x2 =-b/a   

give x1 and x2 are prime ,only possible if a=1


so x1 +x2 =-b/a   

and x1*x2 =c

also given

a+b+c =prime number

or 1+b+c=prime number


put vale of b and c

1-(x1+x2) +x1*x2 =prime number

(x1-1)(x2-1)=prime number

only possible if one bracket is equal to 1

ie x1=2

and x2=3(prime number)

so sum x1+x2=2+3=5

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Badiuddin

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