Q. 33.9( 24 Votes )

# 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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