Q3 of 108 Page 36

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

Let the two zeroes be a and b.

Given:


Sum of squares of zeroes is 40


a2 + b2 = 40


The generalized form of the quadratic equation with sum and product of zeroes a and b is as follows:


x2 – (a + b)x + ab = 0 ………………… (i)


a + b = 8


ab = k


We also know that,


(a + b)2 = a2 + b2 + 2ab


a2 + b2 = (a + b) 2 – 2ab


(a + b) 2 – 2ab = 40


(8)2 – 2k= 40


2k = 64 – 40


2k = 24


k = 12


Therefore the value of k = 12


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