For-what-values-of-m-the-equation-1-m-x-2-2-1-3m-x-1-8m-0-m-R-has-both-roots-positive-

Question Number 17359 by ajfour last updated on 04/Jul/17

For what values of m, the equation

(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0;

m \in R, has both roots positive ?

Commented by ajfour last updated on 04/Jul/17

{book}^{'} s answer :

m \in (- \infty, - 1) \cup [3, \infty)

my answer differed . .

Commented by ajfour last updated on 04/Jul/17

thanks Sir . very precise .

Commented by prakash jain last updated on 04/Jul/17

roots are \frac{- b}{2 a} \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}

- \frac{b}{2 a} lies in between roots

condition for + ve roots > 0

- \frac{b}{2 a} ⩾ 0, α β > 0, D ⩾ 0

\frac{(1 + 3 m)}{(1 + m)} ⩾ 0 \Rightarrow m \in (- \infty, - 1) \cup [- \frac{1}{3}, \infty)

\frac{(1 + 8 m)}{(1 + m)} > 0 \Rightarrow m \in (- \infty, - 1) \cup (- \frac{1}{8}, \infty)

D = 4 {{(1 + 3 m)}^{2} - (1 + m) (1 + 8 m)} ⩾ 0

\Rightarrow m (m - 3) ⩾ 0 \Rightarrow m \in (- \infty, 0] \cup [3, \infty)

a n s w e r

m \in (- \infty, - 1) \cup (- \frac{1}{8}, 0] \cup [3, \infty)

Commented by Tinkutara last updated on 05/Jul/17

ajfour Sir, which book is that ? Can you

please tell its description so that I can

prepare well from it ?

Commented by ajfour last updated on 05/Jul/17

S . K . {Goyal}^{'} s Algebra, Arihant

Prakashan .

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