Question

If the roots of the equation 12x^2+mx+5=0 are in the ratio 3:2 , then m equals to ?

Answer 1

Answer:

P(x): 12x^2 + mx + 5 = 0

Ratio of roots = 3:2

using quadratic equation the roots are ,

{-m +√(m^2-240)}/24 ..........equ[i]

and

{-m-/√(m^2-240)}/24 .......equ(ii)

divide equation one by two , We get

{Let √(m^2 -240) be taken as x}

Therefore , {-m+x}/{-m-x} = 3/2

Or, m = -5x [ cross multiply]

0r, m = -5√(m^2-240)

0r, m^2 = 25 (m^2 -240)

Or, -24m^2 = -6000

0r, m^2 = 250

Or, m = 5√10

Answer 2

Explanation:

Let the roots be α,β

αβ=32

α+β=−m12

αβ=512

α=32β⇒32β2=512

⇒β2=1036⇒β=−10−−√6

α=32β=−10−−√4

m=−12(α+β)

=12(10−−√6+10−−√4)

=510−−√

Hence (D) is the correct answer.