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.

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

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

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

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

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

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

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