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If the sum of the roots of the equation x^2 - 3x + p = 0 is 3, what is the value
If the sum of the roots of the equation x^2 - 3x + p = 0 is 3, what is the value of p?
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If the sum of the roots of the equation x^2 - 3x + p = 0 is 3, what is the value of p?
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The sum of the roots is given by -b/a = 3. Here, -(-3)/1 = 3, so p can be any value.
Questions & Step-by-step Solutions
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Q: If the sum of the roots of the equation x^2 - 3x + p = 0 is 3, what is the value of p?
Solution:
The sum of the roots is given by -b/a = 3. Here, -(-3)/1 = 3, so p can be any value.
Steps: 7
Show Steps
Step 1: Identify the equation given, which is x^2 - 3x + p = 0.
Step 2: Recognize that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by the formula -b/a.
Step 3: In our equation, a = 1 and b = -3.
Step 4: Substitute the values of a and b into the formula: -(-3)/1.
Step 5: Calculate -(-3)/1, which simplifies to 3/1 = 3.
Step 6: Since the sum of the roots is already given as 3, this means our calculation is correct.
Step 7: Notice that the value of p does not affect the sum of the roots, so p can be any value.
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