What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imagina

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Question: What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imaginary?

Options:

Correct Answer: k < 0

Solution:

The discriminant must be less than zero: k^2 - 4*1*9 < 0 leads to k^2 < 36, hence k < 0 or k > 0.

What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imaginary?

What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imaginary?

Step 1: Identify the equation given, which is x^2 + kx + 9 = 0.
Step 2: Understand that the roots of a quadratic equation are imaginary when the discriminant is less than zero.
Step 3: The discriminant (D) for the equation ax^2 + bx + c = 0 is calculated using the formula D = b^2 - 4ac.
Step 4: In our equation, a = 1, b = k, and c = 9. So, the discriminant becomes D = k^2 - 4*1*9.
Step 5: Simplify the discriminant: D = k^2 - 36.
Step 6: Set the discriminant less than zero for the roots to be imaginary: k^2 - 36 < 0.
Step 7: Rearrange the inequality: k^2 < 36.
Step 8: Take the square root of both sides: -6 < k < 6.
Step 9: This means k can be any value between -6 and 6, but not including -6 and 6.

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