If the sum of the roots of the equation x^2 - 6x + k = 0 is 6, what is the value

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Question: If the sum of the roots of the equation x^2 - 6x + k = 0 is 6, what is the value of k? (2020)

Options:

Correct Answer: 9

Exam Year: 2020

Solution:

The sum of the roots is given by -(-6)/1 = 6. The product of the roots is k, and since the sum is correct, k can be any value.

If the sum of the roots of the equation x^2 - 6x + k = 0 is 6, what is the value of k? (2020)

If the sum of the roots of the equation x^2 - 6x + k = 0 is 6, what is the value of k? (2020)

Step 1: Identify the equation given, which is x^2 - 6x + k = 0.
Step 2: Recall the formula for the sum of the roots of a quadratic equation ax^2 + bx + c = 0, which is -b/a.
Step 3: In our equation, a = 1, b = -6, and c = k.
Step 4: Substitute the values into the formula: Sum of the roots = -(-6)/1 = 6.
Step 5: Since the sum of the roots is already given as 6, this confirms our calculation is correct.
Step 6: The value of k does not affect the sum of the roots, so k can be any value.

Quadratic Equations – Understanding the properties of quadratic equations, specifically the relationships between coefficients and roots.
Sum and Product of Roots – Applying Vieta's formulas to find the sum and product of the roots of a quadratic equation.