Q4 of 108 Page 44

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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