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Kavya is told that $x^{2} + k x + 16 = 0$ has equal roots. She finds two possible values of $k$ . What is the sum of the squares of these two values of $k$ ?

Class 10Discriminant and Nature of RootsAlgebra — Quadratics

A113
B128
C143
D256

Step-by-Step Solution

Equal roots:

k^{2} - 64 = 0

, so

k = + / - 8

. Sum of squares =

8^{2} + (- 8)^{2} = 64 + 64 = 128

.

Answer: B) 128

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