Numerical answer
The roots of the equation x² − 14x + k = 0 differ by 4. Find the value of k.
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Answer: 45
Let the roots be a and a+4. Sum of roots = 2a+4 = 14 (since sum of roots of x²−14x+k is 14), giving a = 5. So the roots are 5 and 9. Product of roots = k, so k = 5×9 = 45. Shortcut: for x²−sx+p=0 with roots differing by d, solve 2a+d=s for the smaller root a, then k = a(a+d).
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