Question

if alpha and beta are the zeroes of the polynomial p(x)=6x2-5x+k. such that alpha -beta=1/16hen find the value of the k

Answer 1

i think its alpha - beta = 1/6
but still i am doing it for 1/16

sum of roots = -b/a = 5/6
so alpha + beta = 5/6
and alpha - beta = 1/16
adding two equation
we get
2alpha = 5/6 + 1/16
2alpha = (40+3)/48
alpha = 43/96
putting in first equation
beta = 5/6 - alpha
beta = 5/6 - 43/96
beta = (80-43)/96
beta = 37/96
now, product of roots = c/a
43/96 × 37/96 = k/6
k = 1.035
hope it helps.



for alpha - beta = 1/6
sum of roots = -b/a = 5/6
so alpha + beta = 5/6
and alpha - beta = 1/6
adding two equation
we get
2alpha = 5/6 + 1/6
2alpha = 1
alpha = 1/2
putting in first equation
beta = 5/6 - alpha
beta = 5/6 - 1/2
beta = (5-3)/6
beta = 1/3
now, product of roots = c/a
1/2 × 1/3 = k/6
k = 1
hope it helps.