IIM Bangalore (BBA-DBE) Algebra > Quadratic Equations PYQs

If the equation $(m - 3)x^2 - 2mx + 5m = 0$ has real and positive roots, then the possible value(s) of m lies in:

Regarding the function $f(x)=x^{2}-5 x+1$ and $g(x)=1-x-x^{3}$ on the set of real numbers, which of the following statements is not true?

The roots of the equation $ x^2 + 18x - 703 = 0 $ are given as $ a $ and $ b $, with $ a > b $. The roots of the equation $ x^2 - 10x - 336 = 0 $ are given as $ c $ and $ d $, with $ c > d $. Which of the options below gives the correct relation between $ a $, $ b $, $ c $, and $ d $?