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If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the
If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
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If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
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The sum of the roots is 3 + 4 = 7, hence m = -7.
Questions & Step-by-step Solutions
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Q: If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
Solution:
The sum of the roots is 3 + 4 = 7, hence m = -7.
Steps: 5
Show Steps
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and 4.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -m/a. Here, a = 1 (since the equation is x^2 + mx + n = 0).
Step 3: Calculate the sum of the roots: 3 + 4 = 7.
Step 4: Set the sum of the roots equal to -m: 7 = -m.
Step 5: Solve for m by multiplying both sides by -1: m = -7.
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