Question

If ???? and ???? are zeroes of the polynomial p(x) = 6x2 – 5x + k such that ???? – ???? =1/ 16, find the value of k.

Answer 1

We know
Roots of an equation

R1 = -b + root b^2 - 4ac / 2a
R2 = -b - root b^2 - 4ac / 2a

R1 = -5 + root [25 - 24K ] / 6
R2 = -5 - root [ 25 -24K]/ 6
Thus According to question

R1 -  R2 =  1/16
2 root [25-24K] = 6/16
root [25-24K] = 3/16
25 - 24K = 6/ 256
24 K = 25 - 6/256
24K = 24
K = 1
Thus K = 1