Question

2x^{3}+30xx^{2} +72x=0 solve using zero product property

Answer 1

Answer:

Values of x are: x=0 or x=-3 or x=-12

Step-by-step explanation:

The equation given to solve using zero product property is $2x^3+30x^2+72x=0$

Zero property rule states that if ab=0 then a=0 or b=0

Taking x common from the equation:

$2x^3+30x^2+72x=0\\x(2x^2+30x+72)=0$

Applying zero product rule

$x(2x^2+30x+72)=0\\x=0 \ or \ 2x^2+30x+72=0$

Now, solving $2x^2+30x+72=0$

Using quadratic formula to find value of x

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Putting values

$x=\frac{-30\pm\sqrt{(30)^2-4(2)(72)}}{2(2)} \\ x=\frac{-30\pm\sqrt{324}}{4} \\ x=\frac{-30\pm18}{4} \\ x=\frac{-30+18}{4} \ or \ x=\frac{-30-18}{4} \\x=-3 \ or \ x=-12$

So, Values of x are: x=0 or x=-3 or x=-12