If two (positive) prime numbers are roots of the equation x^2-12x+k=0, what is the value of k?
THXXX
x^2 - 12x + k = 0
By Vieta
The sum of the roots = -(-12) /1 = 12 / 1 = 12
The only two positive primes that sum to 12 are 5 and 7
So we have that
(x - 7) ( x - 5) = 0
x^2 - 7x - 5x + 35 = 0
x^2 - 12x + 35 = 0
So.....k = 35
