Question

Solve the following equation by using formula :

x² + (4 – 3a)x – 12a = 0

Answer 1

x² + (4 – 3a)x – 12a = 0
Here a = 1, b = 4 – 3a, c = -12a
∴ D = b² – 4ac
= (4 – 3a)² – 4 x 1 x (–12a)
= 16 – 24a + 9a² + 48a
= 16 + 24a + 9a² = (4 + 3a)

∴ x = `(-b ± sqrt("D"))/(2a)`

= `(-(4 - 3a) ± sqrt(4 + 3a^2))/(2 xx 1)`

= `(3a - 4 ± 3a + 4)/(2)`

∴ x₁ = `(3a - 4 + 3a + 4)/(2)`

= `(6a)/(2)`
= 3a
and

x₂ = `(3a - 4 - 3a - 4)/(2)`

= `(-8)/(2)`
= –4
∴ Roots are 3a, –4.