2x^4-9x^3=21x^2-26x+12/2x-3
The = sign in your problem is an error;
it should probably be a + sign. So I
used a + sign.
Solving 4th (x^4) order Eqs is a very tedious and complex operation and is
done mostly by trial and error. By using EXCEL Program, i was able to simplify the procedure somewhat.
The process starts by dividing the Eq
by a binomial that gives a zero remainder,using long division: 2x - 3 (given) and x-1.
(2x^4 - 9x^3 + 21x^2 - 26x + 12) / (2x - 3) = x^3 - 3x^2 + 6x - 4,
(x^3 - 3x^2 + 6x - 4) / (x - 1) =
x^2 - 2x + 4,
Since we have reduced the 4th deg. Eq
to 2nd deg., we can use the Quadratic Formula to solve it.
x = (-2 +- sqrt(4 - 16)) / 2 =
(-2 +- 2i * sqrt(3)) / 2 =
x = -1 + i * sqrt(3),
x = -1 - i * sqrt(3),
How many solutions(roots) do we have?
The maximum for a 4th order(degree) Eq
is 4. Let's see:
2x - 3 = 0,
x = 3/2.
x - 1 = 0,
x = 1.
We have 4 solutions:
x = 3/2,
x = 1.
x = -1 - i * sqrt(3),
x = -1 + i * sqrt(3).
The last 2 are Imagenary.
To solve the equation 2x^4 - 9x^3 = 21x^2 - 26x + 12/(2x - 3), we can follow these steps:
1. Simplify the equation by dividing both sides by (2x - 3):
(2x^4 - 9x^3) / (2x - 3) = (21x^2 - 26x + 12) / (2x - 3)
2. Simplify both sides of the equation. Since the equation is a rational equation, we need to find the common denominator and combine the fractions:
To simplify the left side, we can use long division or synthetic division to divide (2x^4 - 9x^3) by (2x - 3). This will give us a quotient and a remainder.
3. Once we have the simplified equation, we can proceed to solve for x by setting the numerator equal to zero:
Numerator of the simplified equation = 0
4. Solve the resulting equation for x. This may involve factoring, using the quadratic formula, or other methods depending on the equation's complexity.
I'll be happy to calculate the solution for you if you provide me with the specific equation or values involved.