What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and

₹0.0

Question: What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?

Options:

Correct Answer: 7

Solution:

Using Vieta\'s formulas, k = 3 + 4 = 7.

What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?

What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?

Step 1: Identify the given quadratic equation, which is x^2 - kx + 12 = 0.
Step 2: Recognize that the roots of the equation are given as 3 and 4.
Step 3: Use Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is equal to -b/a.
Step 4: In our equation, a = 1, b = -k, and c = 12.
Step 5: Calculate the sum of the roots: 3 + 4 = 7.
Step 6: Set the sum of the roots equal to -(-k)/1, which simplifies to k.
Step 7: Therefore, we have k = 7.

No concepts available.