If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of
Practice Questions
Q1
If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?
1
5
-1
-5
Questions & Step-by-Step Solutions
If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?
Correct Answer: -1
Step 1: Identify the roots of the equation, which are given as 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.
Sum of Roots – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a. In this case, the roots are provided, allowing for the calculation of p.
Quadratic Equation – Understanding the standard form of a quadratic equation and how to manipulate it to find coefficients based on given roots.
