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!
'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!
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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.
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.
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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
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
b^2 - 4ac < 0
12^2 - 4(k)(9) < 0
144 - 36k < 0
- 36k < - 144
k > 4