Question

The equation x2 – px – 60 = 0, has two roots ‘a’ and ‘b’ such that (a –
b) = 17 and p > 0. If a series starts with ‘p’ such that the consecutive terms are 4 more than the preceding term is formed, then find the product of 2nd and 4th terms of such series.

Q: Answer-The equation x2 – px – 60 = 0, has two roots ‘a’ and ‘b’ such that (a – b) = 17 and p > 0. If a seri...

Given, x2 px 60 0 Since, sum of roots --p1 So, a b p Since, product of roots of the equation -601 Therefore, ab -60. 1 Or, b -60a And, a b 17. 2 Putting the value of b in equation 2, we get a2 17a 60 0 a2 12a 5a 60 0 aa 12 5a 12 0 a 12a 5 0 a 12, 5 When a 12, then b -5-6012 And, when a 5, then b -12-725 Therefore, a b 12 -5 7 p Therefore, series will be 7, 11, 15, 19 required product 11 19 209