Q7 of 90 Page 2

If the sum of squares of the zeroes of the quadratic polynomial x2 – 8x + k is 40, find k.

Given : p(x) = x2 – 8x + k


α2 + β2 = 40


We have,



and


So,


…(1)


…(2)


Now, if we recall the identities


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


Using the identity, we get


(α + β)2 = α2 + β2 + 2 αβ


(8)2 = + 2(k)


⇒2k = 64 – 40


= = 12


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