Question

Aflati radacinile reale ale polinomului:
P(x)=3x⁴-x²-2
P(x)=x³-5x²+6x
P(x)=27x³-1
P(x)=16x⁴-64

Answer 1

1)  3x⁴- 3x²+2x²-2= 3x²(x²-1) + 2(x²-1) = (x²-1) * (3x²+2)= (x+1)(x-1)(3x²+2)
⇒ (x+1)(x-1)(3x²+2) = 0 ⇒ x+1=0⇒ x=-1 sau x-1=0⇒x=1⇒ x∈{-1,1}

2) x(x²-2x-3x+6) = x[x(x-2) -3(x-2)]= x(x-2)(x-3)
⇒ x(x-2)(x-3)=0⇒ x=o sau x-2=0⇒x=2 sau x-3=0⇒x=3⇒ x∈{0,2,3}

3) (3x-1)(9x²+ 3x+1)=0 ⇒ 3x-1=0⇒ 3x=1⇒x=1/3 ⇒ x∈{1/3}

4) 16(x⁴-4) = 16(x²-2) (x²+2) = 16(x²+2) (x-√2) (x+√2)
⇒16(x²+2) (x-√2) (x+√2) = 0 ⇒ x-√2=0⇒ x=√2 sau x+√2=0⇒ x=-√2
⇒x∈{-√2;√2}