If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)

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Question: If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)

Options:

Correct Answer: -7

Solution:

Using the sum of the roots: p = -(3 + 4) = -7.

If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)

If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)

Step 1: Identify the given quadratic equation, which is x² + px + 12 = 0.
Step 2: Recognize that the roots of the equation are given as 3 and 4.
Step 3: Use the formula for the sum of the roots of a quadratic equation, which is -p/a. Here, a = 1 (the coefficient of x²).
Step 4: Calculate the sum of the roots: 3 + 4 = 7.
Step 5: Since the sum of the roots is equal to -p, we set up the equation: -p = 7.
Step 6: Solve for p by multiplying both sides by -1: p = -7.

Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation.
Sum and Product of Roots – Using the formulas for the sum and product of the roots to find unknown coefficients.