x = 2.236, -2.236 & -6. (to 3 decimal places)
x3 + 6x2 - 5x - 30 = 0
First of all, let us note that as the highest power in the polynomial is to the power of 3, we are expecting to find 3 roots (the real + imaginary roots will equal 3).
Ok, so we need to factor the expression x3 + 6x2 - 5x - 30.
There are different methods to try to factor an expression like this. We are going to split this down into 2 groups (because we can see that we will be able to factor each).
1.x3 + 6x2 &
2. -5x - 30. We can factor out the "-" (minus) here to become: - (5x + 30).
So we have:
(x3 + 6x2) - (5x + 30) = 0
We can factor out "x2" from the first bracket and "5" from the second to get:
x2 (x + 6) -5 (x + 6) = 0
We can now see that "x + 6" is a common factor and so we can rewrite the original expression as:
(x2 - 5) (x + 6) = 0
Now we can solve for the roots of x by making each bracket equal to 0 in turn, so:
x2 - 5 = 0
x2 = 5
x = 51/2 (we have two roots here of course: the square root of 5 & the square root of 5 times -1)
x = 2.236 & -2.236 (to 3 decimal places only)
&
x + 6 = 0
x = -6
Thus all roots are real (none are imaginary) and they are: x = 2.236, -2.236 & -6.
x=16
-4,3 are the roots of this equation, so for the values for which the sum of roots is 1 & product is -12
Doesn't have integer roots. Quadratic formula gives roots as 3.71 and -5.38.
one
The roots are: x = 1 and x = 7 So: 7*1 = 7
This question doesn't explain what you desire as an answer. Yes, the roots will destroy your pipes as they will drive there way through them. If you have roots in your pipes, no idea. May have to replace all the piping or get someone to remove the roots from the piping for you. Tree roots will not enter pipes unless there is a entry point in the pipe. If pipes are properly sealed there is no problem.
No real roots. Imaginary roots as this function does not intersect the X axis.
It has two complex roots.
There are 2 roots to the equation x2-4x-32 equals 0; factored it is (x-8)(x+4); therefore the roots are 8 & -4.
x=16
the roots hold in the soil
I am sorry but this answer is a hard one!
It has roots x = 2.618 and x = 0.38197
No real roots
-4,3 are the roots of this equation, so for the values for which the sum of roots is 1 & product is -12
false
The roots are: x = -5 and x = -9