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 (hint :a, b are zeroes then a²+b²=40)

Answer 1

given:f(x)x²-8x+k

if a & b are zeros then,
a²+b²=40........i

from the f(x)
sum of zeros=-b/a
=-(-8)/1
=8.......ii

product of zeros=c/a
=k......iii

according to the identity
(a+b)²=a²+b²+2ab
(8)²=40+2k{putting the value of i,ii & iii}
64-40=2k
24=2k
12=k