Can someone please help me on this math question
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Can someone please help me on this math question

[From: ] [author: ] [Date: 11-10-31] [Hit: ]
The given equation will have imaginary roots if the discriminate of the quadratic equation is less than 0 (in other words,The given equation will have imaginary roots for any real number k > 4. QED.-For having imaginary roots discriminant has to be negative.......
I'm having a little trouble with this question..
'For what values of k does kx2 + 12x + 9 = 0 have imaginary roots?'

I'd be so grateful if someone could help me out. Please be explanatory and show steps. :)
Thanks so much, I really appreciate it!

-
I am assuming you mean:

kx² + 12x + 9 = 0

If so:

The given equation will have imaginary roots if the discriminate of the quadratic equation is less than 0 (in other words, b² - 4ac < 0). Hence,

b² - 4ac < 0

12² - 4(k)(9) < 0

144 - 36k < 0

144 < 36k

4 < k.

The given equation will have imaginary roots for any real number k > 4. QED.

-
For having imaginary roots discriminant has to be negative.

b^2-4ac<0

(12)^2 - 4(9k)<0
144-36k<0
36k>144
k>4

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sqrt(b^2 - 4ac) < 0

b^2 - 4ac < 0

12^2 - 4(k)(9) < 0

144 - 36k < 0

- 36k < - 144

k > 4
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