Find all the zeroes of the equation.–3x4+ 27x2 + 1200 = 0

Answer 1

To find the zeros of the equation, we can use the fact that a zero of a polynomial equation is a value of x that makes the equation equal to zero.

Given equation: -3x^4 + 27x^2 + 1200 = 0

Factor out a common factor of -3: -3(x^4 - 9x^2 - 400) = 0

Now we have a quadratic equation in the form: ax^2 + bx + c = 0, where a = 1, b = -9, and c = -400.

Let's solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-(-9) ± √((-9)^2 - 4(1)(-400))) / (2(1))

x = (9 ± √(81 + 1600)) / 2

x = (9 ± √(1681)) / 2

x = (9 ± 41) / 2

x1 = (9 + 41) / 2 = 50 / 2 = 25
x2 = (9 - 41) / 2 = -32 / 2 = -16

So the zeroes of the equation are x = 25 and x = -16.