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

What is the value of k if the roots of the equation x^2 - kx + 9 = 0 are real and distinct?

What is the value of k if the roots of the equation x^2 - kx + 9 = 0 are real and distinct?

Step 1: Identify the equation given, which is x^2 - kx + 9 = 0.
Step 2: Recognize that for the roots of a quadratic equation to be real and distinct, the discriminant must be greater than zero.
Step 3: The discriminant (D) for the equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
Step 4: In our equation, a = 1, b = -k, and c = 9.
Step 5: Substitute the values into the discriminant formula: D = (-k)^2 - 4(1)(9).
Step 6: Simplify the expression: D = k^2 - 36.
Step 7: Set the discriminant greater than zero for real and distinct roots: k^2 - 36 > 0.
Step 8: Rearrange the inequality: k^2 > 36.
Step 9: Solve for k by taking the square root: k < -6 or k > 6.

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