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For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is
For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is the value of p?
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Q1
For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is the value of p?
2
-2
3
-3
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The sum of the roots is 1 + (-3) = -2, hence p = -2.
Questions & Step-by-step Solutions
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Q
Q: For the quadratic equation x^2 + px + q = 0, if the roots are 1 and -3, what is the value of p?
Solution:
The sum of the roots is 1 + (-3) = -2, hence p = -2.
Steps: 6
Show Steps
Step 1: Identify the roots of the quadratic equation, which are given as 1 and -3.
Step 2: Calculate the sum of the roots by adding them together: 1 + (-3).
Step 3: Simplify the sum: 1 - 3 = -2.
Step 4: In a quadratic equation of the form x^2 + px + q = 0, the sum of the roots is equal to -p.
Step 5: Since we found the sum of the roots to be -2, we can set -p = -2.
Step 6: To find p, multiply both sides of the equation by -1: p = 2.
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