SOLVE FOR x : ad2x(ax/b + 2c/d) + c2b = 0 - Maths - Quadratic Equations

Question

SOLVE FOR x :
ad2x(ax/b + 2c/d) + c2b = 0

Chetna Khanna · Accepted Answer

$a d^{2} x (\frac{a x}{b} + \frac{2 c}{d}) + c^{2} b = 0 \Rightarrow \frac{a^{2} d^{2} x^{2}}{b} + \frac{2 c a d^{2} x}{d} + c^{2} b = 0 \Rightarrow \frac{a^{2} d^{2} x^{2}}{b} + 2 a c d x + c^{2} b = 0 \Rightarrow a^{2} d^{2} x^{2} + 2 a b c d x + c^{2} b^{2} = 0 \Rightarrow (a d x + b c)^{2} = 0 \Rightarrow (a d x + b c) = 0 \Rightarrow x = \frac{- b c}{a d}$

Thus, the given equation has equal roots which are $- \frac{b c}{a d} and - \frac{b c}{a d}$ .