Question

if alfa and ß are zeros of polynomial p(x)=6x^2-5x+k such that alfa-ß=1/6, find the value of k

Answer 1

we know that

a= alpha b = beta

a - b = 1/6 ......1

and a + b = 5/6 ......2

by solving equation 1 and 2 we get
a = 1 and b = -1/6
it is given in the question that a and b are the zeroes of the equation
so substitute any one the value a or b in the p(x) I am taking the simplest one i. e a =1
so
p (x) = 6/2 -5/2 + k = 0
so now k = -1/2