Question

If the roots of x^2+mx+12=0are in ratio of 1:3 find m

Answer 1

Answer:

let the root be α&β

given that : α/β = 1/3

               ⇒3α=β .....(1)

taking relation between the zeroes ;

 1. sum of the zeroes (α+β) = -b/a

           α + 3α= -m/1                           ∵( from (1))

                 4α= -m  ⇒α= -m/4 ....(2)

2. product of the zeroes (αβ) = c/a

                          α(3α)= 12/1

                           3α²= 12

                             α²= 4

                              α= 2

       ∴  -m/4=2                     ∵( from (2))

       thus, m= -8