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consider two condition `x^2-3x-10<0` and |x-2|<α on a real number x, where...
consider two condition `x^2-3x-10<0` and |x-2|<α on a real number x, where a is a positive real number
i. the range of values of α such that |x-2|<α is a necessary condition for `x^2-3x-10<0` is (A)
2. the range of values α such that |x-2|<α is a sufficient condition for `x^2-3x-10<0` is (B)
1 Answer | add yours
Solve the first inequality:
(-5)(2)=-10 and -5+2=-3
A) For the necessary condition we with to find the range of a for which |x-2| must be true in order for x^2-3x-10 to be true:
In order for -2 < x < 5 to map to 2-a < x < 2+a, a cannot be more than 4 (a<=4)
Consequently, the necessary condition is: a<=4
B) For the sufficient condition we wish to find the range of a for which if |x-2|<a is true then x^2-3x-10<0 is also true:
The magnitude of any value must be positive, therefore:
Consequently, the sufficient condition is: 0<a<=3
Posted by crmhaske on May 24, 2013 at 12:59 PM (Answer #1)
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