If the sum of the roots of the equation x² - k²x + 30kx - 161x - 64 = 0 is zero, then what is the difference of the roots?
Answer
The correct answer is A: 16. Equation: x² + (30k-k²-161)x - 64 = 0. Sum of roots = k²-30k+161 = 0, k²-30k+161=0, k=(30±√(900-644))/2=(30±16)/2=23 or 7.
A.16✓ Correct
B.15
C.18
D.17
Explanation
Equation: x² + (30k-k²-161)x - 64 = 0. Sum of roots = k²-30k+161 = 0, k²-30k+161=0, k=(30±√(900-644))/2=(30±16)/2=23 or 7. Product of roots = -64. If sum=0, roots are r,-r, product=-r²=-64, r=8. Difference = 16.
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