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What is a if ax^2 - 16x + 32 = 0 has only complex roots.

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pqc | Student, Kindergarten | (Level 1) Salutatorian

Posted August 15, 2013 at 2:19 PM via web

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What is a if ax^2 - 16x + 32 = 0 has only complex roots.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 15, 2013 at 2:23 PM (Answer #1)

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The roots of a quadratic equation ax^2 + bx + c = 0 are given by `(-b+-sqrt(b^2-4ac))/(2a)` . They are complex when b^2 - 4ac < 0

For the equation ax^2 - 16x + 32 = 0, the roots are complex when (-16)^2 - (4*a*32) < 0

=> 256 < 128a

=> 2 < a

The roots of the given equation are complex for `a in (-oo, 2)`

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