Question: If the roots of the equation x^2 - px + q = 0 are 3 and 4, what is the value of p?
Options:
7
12
9
10
Correct Answer: 7
Solution:
The sum of the roots is p = 3 + 4 = 7.
If the roots of the equation x^2 - px + q = 0 are 3 and 4, what is the value of
Practice Questions
Q1
If the roots of the equation x^2 - px + q = 0 are 3 and 4, what is the value of p?
7
12
9
10
Questions & Step-by-Step Solutions
If the roots of the equation x^2 - px + q = 0 are 3 and 4, what is the value of p?
Correct Answer: 7
Step 1: Identify the roots of the equation. The roots given are 3 and 4.
Step 2: Recall that for a quadratic equation of the form x^2 - px + q = 0, the sum of the roots is equal to p.
Step 3: Calculate the sum of the roots: 3 + 4.
Step 4: Add the numbers: 3 + 4 = 7.
Step 5: Conclude that the value of p is 7.
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 the equation ax^2 + bx + c = 0 is given by -b/a, which in this case simplifies to p.
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