If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of

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Question: If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of p?

Options:

Correct Answer: 5

Solution:

Using the sum of roots formula, p = -(4 + (-1)) = -3.

If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of p?

If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of p?

Step 1: Identify the roots of the equation. The roots given are 4 and -1.
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 (since it's x^2), b = p, and c = q.
Step 4: Calculate the sum of the roots: 4 + (-1) = 3.
Step 5: Set the sum of the roots equal to -b/a: 3 = -p/1.
Step 6: Rearrange the equation to find p: -p = 3.
Step 7: Multiply both sides by -1 to solve for p: p = -3.

Sum of Roots – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a.
Quadratic Equation – Understanding the standard form of a quadratic equation and its properties.