Question

For what values of k does kx²+12x+9=0 have imaginary roots?

Answer:

K is greater than 4.

For the given equation to have imaginary roots, the discriminant has to be negative.
Therefore,
D = b² - 4ac < 0
⇒ 12² - 4(k)(9) < 0
⇒ 144 - 36k < 0
⇒ 144 < 36k
⇒ 144/36 < k
⇒ 4 < k
Therefore, for all values of K greater than 4, this equation will have imaginary roots.


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