5. If x^2 + 2x -15 = -m, where m is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?
A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7
This was little trickier but here is my approach
We need to know Probability that m is greater than 0.
Integer is from -10 to 10 inclusive.
Consider value of m greater than 0 only and put in the value in the given eqn
For ex let us say m= 2, the eqn becomes
x^2+2x -15= -2----. x^2+ 2x -13=0 -----> Eqn will have roots of the form -b+/- \sqrt{b^2-4ac}/ 2
We see that for m= 7, we get the eqn as x^2+ 2x -8 =0, Solving for x we get,
x = 4 or -2.
This seems to be the only case where the eqn gives us 2 real roots and therefore looking at option choices selected B (assuming other 2 cases will be for value of m between -10 to 0)
Ans Choice B
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