what is the root of 4x to the 4th power + 8x to the 3rd power - 13x to the 2nd power -2x +3
I think you mean
(√(4x))^4 + 8x^3 - 13x^2 - 2x + 3
which is
16x^2 + 8x^3 - 13x^2 - 2x + 3
= 8x^3 + 3x^2 - 2x + 3
Now what about it?
What do want done with it?
I need the roots of 4x^4+8x^3-13x^2-2x+3
Read your first line, can you see how it can be misinterpreted?
so let
f(x) = 4x^4+8x^3-13x^2-2x+3
try x = ±1, ±3
f(1) = 0, so x-1 is a factor,
I then used synthetic division to show that
4x^4+8x^3-13x^2-2x+3 = (x-1)(4x^3 + 12x^2 - x - 3)
but (4x^3 + 12x^2 - x - 3)
= 4x^2(x+3) - (x+3)
= (x+3)(4x^1 - 1)
= (x+3)*2x-1)(2x+1)
so for
4x^4+8x^3-13x^2-2x+3 = 0
(x-1)x+3)(2x+1)(2x-1) = 0
x = 1, -3, ±1/2
To find the root of the given polynomial, we need to solve for x such that the polynomial equals zero. In other words, we are looking for the values of x that make the equation true.
The given polynomial is:
4x^4 + 8x^3 - 13x^2 - 2x + 3 = 0
Unfortunately, finding the exact algebraic solutions for polynomials of degree four or higher can be quite complex. In this case, we'll need to use numerical approximation methods to estimate the roots.
One approach is to use a graphing calculator or computer software to graph the polynomial and look for the x-intercepts. Another common numerical method is to use a technique called root-finding algorithms, such as the Newton-Raphson method or the bisection method.
If you have access to a graphing calculator or suitable software, you can input the polynomial equation and find the x-intercepts directly. This will provide you with approximate values for the roots. However, if you don't have access to these tools, you might consider using numerical root-finding algorithms implemented in programming languages or online tools.
Overall, finding the exact roots of a given polynomial can be quite challenging, and it often requires numerical approximation methods.