The roots of the quadratic equation x^2 -2015x + k =0 are prime numbers ,then k is equal to : A) 4022 B)4026 C)2017 D)2016 PLEASE HELP I HAVE FULL PAPER TEST !! CLASS 11-12 IIT-JEE
Answers
Given : The roots of the quadratic equation x² -2015x + k =0 are prime numbers ,
To Find : k is equal to :
A) 4022 B)4026 C)2017 D)2016
Solution:
x² -2015x + k =0
Sum of roots = -(-2015) = 2015
roots are prime
Product of roots = k
4022 = 2 x 2011
sum of roots = 2 + 2011 = 2013 ≠2015
4026 = 2 x 3 x 11 x 61
Not a product of prime numbers
sum of roots = 2 + 2013= 2015 = 2015
but 2013 is not prime
2017 = 1 x 2017 but 1 is not prime
2016 = 2⁵ x 3² x 7
Not a product of prime numbers
Hence none of these satisfy
However
k can b 4026
if roots are 2 and 2013
but 2013 is not prime
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