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
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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
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
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