how do you solve 3x^4 + 11x^3=4x^2
To solve the equation 3x^4 + 11x^3 = 4x^2, you can follow these steps:
Step 1: Rearrange the equation to have zero on one side:
3x^4 + 11x^3 - 4x^2 = 0
Step 2: Factor the equation:
x^2(3x^2 + 11x - 4) = 0
Step 3: Solve for x using the Zero Product Property:
x^2 = 0 or 3x^2 + 11x - 4 = 0
Step 4: Solve the first equation:
x^2 = 0
x = 0 (since the square of zero is zero)
Step 5: Solve the quadratic equation:
3x^2 + 11x - 4 = 0
You can use the quadratic formula to find the solutions of this equation:
x = (-b +/- √(b^2 - 4ac)) / (2a)
For this equation, a = 3, b = 11, and c = -4. Substituting these values, we have:
x = (-(11) +/- √((11)^2 - 4(3)(-4))) / (2(3))
x = (-11 +/- √(121 + 48)) / 6
x = (-11 +/- √169) / 6
x = (-11 +/- 13) / 6
This gives us two potential solutions:
x = (-11 + 13) / 6 = 2 / 6 = 1/3
x = (-11 - 13) / 6 = -24 / 6 = -4
Therefore, the solutions to the equation 3x^4 + 11x^3 = 4x^2 are x = 0, x = 1/3, and x = -4.