Question

Find all roots x^3 + 7x^2 + 12x = 0

Answer 1

Answer:

Therefore the THREE roots are

$x=0\ or\ x=-3\ or x=-4$

Step-by-step explanation:

Given:

$x^{3}+7x^{2} +12x= 0$

To Find:

All  the Roots = ?

Solution:

As the degree of the polynomial is THREE then the number of root are also THREE.

$x^{3}+7x^{2} +12x= 0\\\\x(x^{2}+7x +12)= 0\\\\x=0\\or\\x^{2}+7x +12= 0$

Now one root is Zero For other we need to Factorize

So by Splitting the middle term

i.e Factor of 12 such that sum should be 7

i.e 3 × 4 = 12  and 3 + 4 = 7

∴ $x^{2}+7x +12= 0\\x^{2}+3x+4x +12= 0\\x(x+3)+4(x+3)=0\\(x+3)(x+4)=0\\\\x+3=0\ or\ x+4 = 0\\\\\therefore x=-3\ or x=-4\ \textrm{Which are the roots}$

Therefore the THREE roots are

$x=0\ or\ x=-3\ or x=-4$