Question

find all square roots! x^5 + 2x^3 - 3x = 0

Answer 1

is it find the roots or is this a square root expression?

Answer 2

so like first step you can factorizing out the x and will get

x(x^4 +2x^2 -3) =0

x_1 =0 will be the first root

for x^4 +2x^2 -3 =0 so in this case you need note the x^2 = y and hence will get an quadratic equation in y

y^2 +2y -3 =0 so what you can factorize it like (y +3)(y -1) =0 and now you make first parentheses equal zero so

y+3=0 --- y=-3
and the second ,so y-1=0 --- y=1

so than now there is x^2 = -3 so x_2,3 =+/- sqrt(-3) = +/- isqrt3
and make x^2 =1 so x_4,5 = +/- sqrt(1) = +/- 1

so than (0,+/- isqrt3 , +/- 1 ) are the roots of this equation the grade 5