Find the discriminant of the equation:

\[ 9x^2 + 12x + 4 = 0 \]

t h e d i scr iminan t o f a x 2 + b x + c = 0 : Δ = b 2 − 4 ⋅ b ⋅ c − − − − − − − − − − − − − − − − − − − − − − − − − − − 9 x 2 + 12 x + 4 = 0 ⇒ Δ = 1 2 2 − 4 ⋅ 9 ⋅ 4 = 144 − 144 = 0 Δ = 0 ⇒ x 0 ​ = − 2 a b ​ = − 2 ⋅ 9 12 ​ = − 2 ⋅ 3 ⋅ 3 2 ⋅ 2 ⋅ 3 ​ = − 3 2 ​ A n s . T h e d i scr iminan t i s Δ = 0

Answered by kate200468 | 2024-06-10

9 x 2 + 12 x + 4 = 0 ( 3 x ) 2 + 2 ⋅ 3 x ⋅ 2 + 2 2 = 0 ( 3 x + 2 ) 2 = 0 ⟺ 3 x + 2 = 0 3 x = − 2 / : 3 x = − 3 2 ​ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ( a + b ) 2 = a 2 + 2 ab + b 2

Answered by Anonymous | 2024-06-10

The discriminant of the equation 9 x 2 + 12 x + 4 = 0 is Δ = 0 , indicating that there is exactly one real root. The root can be found using the formula x 0 ​ = − 2 a b ​ , resulting in x = − 3 2 ​ .
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Answered by kate200468 | 2025-06-15