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If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value
If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of n?
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Q1
If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of n?
-3
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Using Vieta's formulas, the product of the roots is n = 1 * (-3) = -3.
Questions & Step-by-step Solutions
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Q
Q: If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of n?
Solution:
Using Vieta's formulas, the product of the roots is n = 1 * (-3) = -3.
Steps: 5
Show Steps
Step 1: Identify the roots of the quadratic equation. The roots given are 1 and -3.
Step 2: Recall Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the product of the roots (r1 and r2) is equal to c/a.
Step 3: In our equation x^2 + mx + n = 0, the coefficient a is 1 (since it's x^2), and c is n.
Step 4: Calculate the product of the roots: 1 * (-3) = -3.
Step 5: According to Vieta's formulas, this product is equal to n. Therefore, n = -3.
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