What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots 3 an

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Question: What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots 3 and -3? (2022)

Options:

Correct Answer: 6

Exam Year: 2022

Solution:

Using Vieta\'s formulas, the sum of the roots is 0, so k = -0 = 0. The product of the roots is 9, confirming k = 6.

What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots 3 and -3? (2022)

What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots 3 and -3? (2022)

Step 1: Identify the given quadratic equation, which is x^2 + kx + 9 = 0.
Step 2: Recognize that the roots of the equation are given as 3 and -3.
Step 3: Use Vieta's formulas, which tell us that the sum of the roots (3 + -3) equals -k.
Step 4: Calculate the sum of the roots: 3 + (-3) = 0.
Step 5: Set the sum equal to -k: 0 = -k.
Step 6: Solve for k: k = 0.
Step 7: Now, use Vieta's formulas again to find the product of the roots, which is 3 * -3 = -9.
Step 8: According to Vieta's formulas, the product of the roots is also equal to 9, which confirms the equation.
Step 9: Since the product of the roots is correct, we can conclude that k = 0.

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