Question: The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?
Options:
1
5
-1
-5
Correct Answer: 5
Solution:
Using the sum of roots: p = -(3 + (-2)) = -1.
The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of
Practice Questions
Q1
The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?
1
5
-1
-5
Questions & Step-by-Step Solutions
The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and -2.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p. The sum of the roots is 3 + (-2).
Step 3: Calculate the sum of the roots: 3 + (-2) = 1.
Step 4: Since the sum of the roots is equal to -p, we set up the equation: -p = 1.
Step 5: To find p, multiply both sides of the equation by -1: p = -1.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Sum of Roots – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a.
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