What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022

What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022)

What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022)

Step 1: Identify the equation given, which is x² + kx + 16 = 0.
Step 2: Understand that for a quadratic equation to have no real roots, the discriminant must be less than zero.
Step 3: The discriminant formula for the equation ax² + bx + c is given by D = b² - 4ac.
Step 4: In our equation, a = 1, b = k, and c = 16.
Step 5: Substitute the values into the discriminant formula: D = k² - 4*1*16.
Step 6: Simplify the expression: D = k² - 64.
Step 7: Set the discriminant less than zero for no real roots: k² - 64 < 0.
Step 8: Rearrange the inequality: k² < 64.
Step 9: Take the square root of both sides: -8 < k < 8.
Step 10: This means k must be less than -8 or greater than 8.

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