Question

9x⁴-3x²+1

Answer 1

Simplifying the equation:

We are given the bi-quadratic equation:

9x⁴-3x²+1

to factorise this equation, we will convert it to a quadratic equation and factor it from there

in the given equation, let x² = y

now, the equation looks like:

9y² - 3y + 1

Finding the Factors (in terms of y):

Using the quadratic formula: x = -b±√(b²-4ac) / 2a

replacing the variables in the equation

y = [-(-3) ± √[(-3)² - 4(9)(1)]]/2(9)

y= [3 ± √-27]/18

y = (1 ± √-3 / 6)

The 2 solutions are:

y = (1 + √-3 / 6)        and     y = (1 - √-3 / 6)

Finding the values of 'x':

Since y = x²:

x² = (1 + √-3 / 6)        and     x² = (1 - √-3 / 6)

taking the square root of both sides

x = √(1 + √-3 / 6)        and     x = √(1 - √-3 / 6)

As we can see, the given equation has complex roots and cannot be simplified further