# Find those values of k for which the roots of the equation x2 + 5kx + 16 = 0 are not real.

When we compare the above quadratic equation with the generalized one we get,

ax2 + bx + c = 0

a = 1

b = 5k

c = 16

For the quadratic equations to have imaginary [not real] roots,

b2 – 4ac < 0 for imaginary [not real] roots

(5k) 2 – (4 × 16 × 1) > 0

25k 2 – 64 < 0

25k 2 < 64

k 2 < 64/25

k <± 8/5

Therefore the range of k values for roots to be imaginary are:

-8/5 < k < 8/5

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