If sum of the squares of zeroes of the quadratic . . .

Question : If sum of the squares of zeroes of the quadratic polynomial 6x²+x+k is 25/36, then the value of k is 

a) 4

b) -4

c) 2

d) -2

Doubt by Zoha

Solution : 

6x²+x+k
a=6
b=1

c=k
so, 
α+β=-b/a
α+β=-1/6

αβ=c/a

αβ=k/6

α²+β²= 25/36 (Given)
α²+β²=(α+β)²-2αβ

25/36 = (-1/6)²-2(k/6)
25/36 =1/36-k/3
25/36-1/36 = -k/3
(25-1)/36 = -k/3

24/36 = -k/3
2/3 = -k/3

2=-k
k = -2

Hence, d) -2, is the correct option. 

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