If p q are chosen randomly from the set {1, 2, 3, 4, - Maths - Probability

Question

If p & q are chosen randomly from the set {1, 2, 3, 4, 5, 6, 7,
8, 9, 10} with replacement Determine
the probability that the roots of the equation x2+ px + q = 0 are
real

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

x2+px+q=0For real rootsD≥0p2-4q≥0p2≥4qFor q=1P=2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 or 10Probability of this event=110×910For q=2P= 3 , 4 , 5 , 6 , 7 , 8 , 9 or 10Probability of this event=110×810For q=3P=  4 , 5 , 6 , 7 , 8 , 9 or 10Probability of this event=110×710For q=4P= 4,5 , 6 , 7 , 8 , 9 or 10Probability of this event=110×710For q=5P=5, 6 , 7 , 8 , 9 or 10Probability of this event=110×610For q=6P= 5 , 6 ,7 , 8 , 9 or 10Probability of this event=110×610For q=7P= 6 , 7 , 8 , 9 or 10Probability of this event=110×510For q=8P= 6 , 7 , 8 , 9 or 10Probability of this event=110×510For q=9P= 6 , 7 , 8 , 9 or 10Probability of this event=110×510For q=10P=  7 , 8 , 9 or 10Probability of this event=110×410Adding probability of all these events :1100 9+8+7+7+6+6+5+5+5+4=62100=0
62   ANS
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If p & q are chosen randomly from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with replacement. Determine the probability that the roots of the equation x2+ px + q = 0 are real.

If p & q are chosen randomly from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with replacement. Determine
the probability that the roots of the equation x2+ px + q = 0 are real.