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If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value o
If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?
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Q1
If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?
-5
-6
-7
-8
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The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.
Questions & Step-by-step Solutions
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Q
Q: If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?
Solution:
The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.
Steps: 7
Show Steps
Step 1: Identify the roots of the equation, which are given as -2 and -3.
Step 2: Use the formula for the sum of the roots, which is -m. Calculate the sum: -2 + (-3) = -5.
Step 3: Since the sum of the roots is -5, we have -m = -5. Therefore, m = 5.
Step 4: Use the formula for the product of the roots, which is n. Calculate the product: (-2) * (-3) = 6.
Step 5: Now we have m = 5 and n = 6.
Step 6: Add m and n together: m + n = 5 + 6.
Step 7: Calculate the final result: 5 + 6 = 11.
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