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

Question : If the sum of the squares of zeroes of the quadratic polynomial f(x)=x²-8x+k is 40, find the value of k.

Doubt by Nevaeh

Solution : 

α²+β²=40 (Given)

f(x)=x²-8x+k

a = 1

b = -8

c = k

α+β=-b/a
α+β=-(-8)/1
α+β=8 — (1)

αβ=c/a

αβ=k/1
αβ=k — (2)

α²+β²=40
(α+β)²-2αβ=40
(8)²-2(k)=40
64-2k=40

64-40=2k
24=2k
24/2=k
k=12

Hence, the required value of k is 12.

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Similar 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