Answer to Question #275334 in Algebra for Good heart

Question

I. Solve polynomial equation using formula method

3x² +9x + 7=0

Ii. Solve polynomial equation using factorization method

X³+2x² ‐ 9x -18=0

Answer 1

i.

$$3x² +9x + 7=0$$

$$D=(9)^2-4(3)(7)=-3$$

$$x=\dfrac{-9\pm\sqrt{-3}}{2(3)}=-\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{6}i$$

$$\{-\dfrac{3}{2}-\dfrac{\sqrt{3}}{6}i,-\dfrac{3}{2}+\dfrac{\sqrt{3}}{6}i\}$$

ii.

$$x^3+2x^2 -9x-18=0$$

$$(x^3+2x^2)-(9x+18)=0$$

$$x^2(x+2)-9(x+2)=0$$

$$(x+2)(x^2-9)=0$$

$$(x+2)(x+3)(x-3)=0$$

$$x_1=-2, x_2=-3, x_3=3$$

$$\{-3, -2, 3\}$$