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If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of
If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?
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If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?
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Using the sum of roots: p = -(3 + (-2)) = -1.
Questions & Step-by-step Solutions
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Q: If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?
Solution:
Using the sum of roots: p = -(3 + (-2)) = -1.
Steps: 5
Show Steps
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.
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