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If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?
If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?
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If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?
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Using Vieta's formulas, if one root is 3, the other root is 7 - 3 = 4. Thus, k = 3 * 4 = 12.
Questions & Step-by-step Solutions
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Q
Q: If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?
Solution:
Using Vieta's formulas, if one root is 3, the other root is 7 - 3 = 4. Thus, k = 3 * 4 = 12.
Steps: 7
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: According to Vieta's formulas, the sum of the roots of the equation is equal to the coefficient of x (which is -(-7) = 7).
Step 4: If one root is 3, we can find the other root by subtracting 3 from the sum of the roots: 7 - 3 = 4.
Step 5: Now we have both roots: 3 and 4.
Step 6: The product of the roots (which is equal to k) is found by multiplying the two roots together: 3 * 4 = 12.
Step 7: Therefore, the value of k is 12.
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