What are the real and complex solutions of the polynomial equation?%0D%0A%0D%0Ax4−29x2=−100
To find the real and complex solutions of the polynomial equation x^4 - 29x^2 = -100, we can rewrite it as:
x^4 - 29x^2 + 100 = 0
Let's solve this equation:
We can substitute y = x^2:
y^2 - 29y + 100 = 0
Factorizing the quadratic equation:
(y - 25)(y - 4) = 0
From here, we get two possible values for y:
y = 25 or y = 4
Substituting back x^2 for y in each equation:
x^2 = 25 or x^2 = 4
Taking the square root of both sides:
x = ±5 or x = ±2
Therefore, the real solutions are x = 5, x = -5, x = 2, and x = -2.