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If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value
If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?
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If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?
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The sum of the roots is 3 + (-3) = 0, so b = -0.
Questions & Step-by-step Solutions
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Q: If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?
Solution:
The sum of the roots is 3 + (-3) = 0, so b = -0.
Steps: 5
Show Steps
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and -3.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -b/a. Here, a = 1 (since the equation is x^2 + bx + 9 = 0).
Step 3: Calculate the sum of the roots: 3 + (-3) = 0.
Step 4: Set the sum of the roots equal to -b/a. Since a = 1, this simplifies to 0 = -b/1, or 0 = -b.
Step 5: Solve for b. If 0 = -b, then b = 0.
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