Question

If λ be the ratio of the roots of the quadratic equation in x, 3m²x² + m(m – 4)x + 2 = 0, then the least value of m for which λ
+ 1/λ = 1,
is:
(A) 2 – √3 (B) 4 – 3√2
(C) –2 + √2 (D) 4 – 2√3

Answer 1

m = 4 ± 2√6 ( as per your question) a = 1

4 - 3√2  ( as per JEE exam) when  a + 1/a = 1

Step-by-step explanation:

3m²x²  + m(m-4)x + 2 = 0

a is the ratio of roots & a = 1

=> Roots are Equal

Roots would be equal if D = 0

=>  (m(m-4))² - 4*3m²*2 = 0

Dividing by m²

=> (m-4)² - 24 = 0

=> m² + 16 - 8m - 24 = 0

=> m²  - 8m - 8 = 0

=> m = (8  ± √8² + 32)/2

=> m = 4 ± 2√6