Question: For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)
Options:
0
4
-4
2
Correct Answer: -4
Exam Year: 2022
Solution:
Using the sum of roots: 2 + (-2) = -p, hence p = 0.
For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (202
Practice Questions
Q1
For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)
0
4
-4
2
Questions & Step-by-Step Solutions
For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)
Step 1: Identify the equation given, which is x² + px + 4 = 0.
Step 2: Recognize that the roots of the equation are given as 2 and -2.
Step 3: Use the formula for the sum of the roots of a quadratic equation, which states that the sum of the roots (r1 + r2) is equal to -p.
Step 4: Calculate the sum of the roots: 2 + (-2) = 0.
Step 5: Set the sum of the roots equal to -p: 0 = -p.
Step 6: Solve for p by multiplying both sides by -1: p = 0.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Sum and Product of Roots – Applying the formulas for the sum and product of the roots of a quadratic equation to find unknown coefficients.
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