Question

34.) Find the roots of equation , if they exist, by applying the quadratic formula :

$3a {}^{2} x {}^{2} + 8abx + 4b {}^{2} = 0$


, a # 0

Answer 1

Given Equation is 3a^2x^2 + 8abx + 4b^2 = 0.

Here, a = 3a^2, b = 8ab, c = 4b^2.

∴ D = b^2 - 4ac

      = (8ab)^2 - 4(3a^2)(4b^2)

      = 64a^2b^2 - 48a^2b^2

      = 16a^2b^2

(i)

$=>x=\frac{-b+ \sqrt{D}}{2a}$

$=>\frac{-(8ab)+\sqrt{(16a^2b^2)}}{6a^2}$

$=>\frac{-8ab+\sqrt{(4ab)^2}}{6a^2}$

$=>\frac{-8ab+4ab}{6a^2}$

$=>\frac{-4ab}{6a^2}$

$=>-\frac{2b}{3a}$

(ii)

$=>x=\frac{-b-\sqrt{D}}{2a}$

$=>\frac{-(8ab)-\sqrt{16a^2b^2}}{6a^2}$

$=>\frac{-8ab-4ab}{6a^2}$

$=>\frac{-12ab}{6a^2}$

$=>-\frac{2b}{a}$

Therefore, the roots of the Equation:

$=>x=\boxed{-\frac{2b}{3a},-\frac{2b}{a}}$

Hope it helps!