If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value
Practice Questions
Q1
If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p? (2020)
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Questions & Step-by-Step Solutions
If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p? (2020)
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 have -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.
Sum of Roots – Using the formula for the sum of the roots of a quadratic equation, which states that for an equation ax^2 + bx + c = 0, the sum of the roots is -b/a.
