Question: If one root of the quadratic equation x^2 + px + q = 0 is 3, and the other root is -1, what is the value of p? (2021)
Options:
2
4
6
8
Correct Answer: 2
Exam Year: 2021
Solution:
The sum of the roots is 3 + (-1) = 2, hence p = -2.
If one root of the quadratic equation x^2 + px + q = 0 is 3, and the other root
Practice Questions
Q1
If one root of the quadratic equation x^2 + px + q = 0 is 3, and the other root is -1, what is the value of p? (2021)
2
4
6
8
Questions & Step-by-Step Solutions
If one root of the quadratic equation x^2 + px + q = 0 is 3, and the other root is -1, what is the value of p? (2021)
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and -1.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p (where p is the coefficient of x).
Step 3: Calculate the sum of the roots: 3 + (-1) = 2.
Step 4: Set the sum of the roots equal to -p: 2 = -p.
Step 5: Solve for p by multiplying both sides by -1: p = -2.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Roots of Quadratic Equations – Identifying and using the properties of the roots, such as their sum and product, to find unknown coefficients.
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