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If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value o
If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k? (2023)
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If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k? (2023)
6
9
12
15
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Using the root 3 in the equation: 3^2 - 7*3 + k = 0, we get k = 6.
Questions & Step-by-step Solutions
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Q
Q: If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k? (2023)
Solution:
Using the root 3 in the equation: 3^2 - 7*3 + k = 0, we get k = 6.
Steps: 8
Show Steps
Step 1: Start with the quadratic equation: x^2 - 7x + k = 0.
Step 2: We know that one root of the equation is 3.
Step 3: Substitute 3 for x in the equation: 3^2 - 7*3 + k = 0.
Step 4: Calculate 3^2, which is 9.
Step 5: Calculate 7*3, which is 21.
Step 6: Now the equation looks like: 9 - 21 + k = 0.
Step 7: Simplify the left side: 9 - 21 equals -12, so we have -12 + k = 0.
Step 8: To find k, add 12 to both sides: k = 12.
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