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If the quadratic equation x^2 - 8x + 15 = 0 is solved, what are the roots? (2022
If the quadratic equation x^2 - 8x + 15 = 0 is solved, what are the roots? (2022)
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Q1
If the quadratic equation x^2 - 8x + 15 = 0 is solved, what are the roots? (2022)
3 and 5
2 and 6
1 and 7
4 and 4
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Factoring gives (x - 3)(x - 5) = 0, hence the roots are 3 and 5.
Questions & Step-by-step Solutions
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Q
Q: If the quadratic equation x^2 - 8x + 15 = 0 is solved, what are the roots? (2022)
Solution:
Factoring gives (x - 3)(x - 5) = 0, hence the roots are 3 and 5.
Steps: 7
Show Steps
Step 1: Start with the quadratic equation: x^2 - 8x + 15 = 0.
Step 2: Look for two numbers that multiply to 15 (the constant term) and add up to -8 (the coefficient of x).
Step 3: The numbers -3 and -5 multiply to 15 and add up to -8.
Step 4: Rewrite the quadratic equation using these numbers: (x - 3)(x - 5) = 0.
Step 5: Set each factor equal to zero: x - 3 = 0 and x - 5 = 0.
Step 6: Solve for x in each equation: x = 3 and x = 5.
Step 7: The roots of the equation are 3 and 5.
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