Question

Find all the zeroes of the equation.

–3x4+ 27x2 + 1200 = 0

Answer 1

To find the zeroes of the equation -3x⁴+ 27x² + 1200 = 0, we can solve it by using the quadratic formula. The solutions are x = -2 and x = 20.

Step-by-step explanation:

To find the zeroes of the equation -3x4+ 27x2 + 1200 = 0, we can solve it by factoring or by using the quadratic formula. Factoring is not feasible in this case, so we will use the quadratic formula.

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.

For this equation, a = -3, b = 27, and c = 1200. Plugging these values into the quadratic formula, we get x = (-27 ± √(27² - 4(-3)(1200))) / (2(-3)). This gives us two solutions: x = -2 and x = 20.

Answer 2

`x=\pm5,\ x=\pm4i`

Step-by-step explanation:

`-3x^4+27x^2+1200=0`

Divide each side by
`-3`

`x^4-9x^2-400=0\\x^4-25x^2+16x^2-400=0\\x^2(x^2-25)+16(x^2-25)=0\\(x^2-25)(x^2+16)`

When
`x^2-25=0`

`x^2=25`

Take square root of both sides

`x=\pm√(25)\\x=\pm5`

`when\ x^2+16=0\\x^2=-16\\x^2=16x^2\ (as\ i^2=-1)`

take square root of both side

`x=\pm√( 16i^2)\\x=\pm4i`