Question #9692a

1 Answer
Nghi N.
Sep 27, 2015

Find k so that the quadratic equation# kx^2 + 8x +5# has real roots.

Explanation:

The Determinant must #>= 0# in order for a quadratic equation to have real roots.
#D = b^2 - 4ac = 64 - 20 k >= 0#
#20 k <= 64# --> #k <= 16/5.#

Check.
k = 1 --> #x^2 + 8x + 5# --> D = 64 - 20 = 44 > 0. OK
k = 4 --> #4x^2 + 8x + 5# --> D = 64 - 80 < 0. OK

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