Prove that the equation 2mx square-3 (M + 2) x + m + 4 = 0 (M is a real number) must have a real root

Prove that the equation 2mx square-3 (M + 2) x + m + 4 = 0 (M is a real number) must have a real root

The discriminant △ = [3 (M + 2)] and#178; - 4 × 2m × (M + 4) = 9m and#178; + 36m + 36-8m and#178; - 32m = m and#178; + 4m + 36
=(m+2）²+32
No matter what value m is, there is always △ 0
The equation 2mx square-3 (M + 2) x + m + 4 = 0 (M is a real number) must have a real root

Calculation: 3x ^ 3 × (- 1 / 9x ^ 2)

Original form
=3×(-1/9）×x^3/x^2
=-1/3*x

Factorization factor 6x ^ 3-9x ^ 2 + 3x

6X^3-9X^2+3x =6X^3-6X^2-3x^2+3x =6x^2(x-1)-(3x^2-3x) =6x^2(x-1)-3x(x-1) =(6x^2-3x)(x-1) =3x(2x-1)(x-1)