If p and q are chosen randomly from the set {1, 2,

Question

If p and 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 equation x2 + px + q = 0 are real.

Aditi Chauhan · Accepted Answer

Hello Student,Please find the answer to your questionThe required probability = 1 &ndash; (Probability of the event that the roots of x2 + px + q = 0 are non &ndash; real if and only ifp2 &ndash; 4q < 0 i.e. if p2 < 4q.We enumerate the possible values of p and q, for which this can happen in the following table.qPNumber of pairs p, q11121, 2,231, 2, 3341, 2, 3351, 2, 3, 4461, 2, 3, 4471, 2, 3, 4, 5581, 2, 3, 4, 5591, 2, 3, 4, 55101, 2, 3, 4, 5, 66Thus, the number of possible pairs = 38. Also, the total number of possible pairs is 10 x 10 = 100.&there4; The required probability= 1 &ndash; 38/ 100 = 1 &ndash; 0.38 = 0.62ThanksAditi ChauhanaskIITians Faculty

Algebra> If p and q are chosen randomly from the s...

If p and 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 equation x2 + px + q = 0 are real.

Simran Bhatia , 10 Years ago

Aditi Chauhan

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q	P	Number of pairs p, q
1	1	1
2	1, 2,	2
3	1, 2, 3	3
4	1, 2, 3	3
5	1, 2, 3, 4	4
6	1, 2, 3, 4	4
7	1, 2, 3, 4, 5	5
8	1, 2, 3, 4, 5	5
9	1, 2, 3, 4, 5	5
10	1, 2, 3, 4, 5, 6	6

Algebra> If p and q are chosen randomly from the s...

If p and 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 equation x2 + px + q = 0 are real.

Simran Bhatia , 10 Years ago

Aditi Chauhan

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Ask a Doubt

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