Question

Solve for the roots of x in each of the equations below.

a. x4 - 81 = 0
b. x4 + 10x2 + 25 = 0
c. x4 - x2 - 6 = 0

Answer 1

Answer: a) x = {-3, 3, -3i, 3i}

b) x = {-√5, √5}

c) x = {-√3, √3, -i√2, i√2}

Explanation:

`a)\ x^4-81=0\\\\(x^2-9)(x^2+9)=0\\\\x^2=9\quad and\quad x^2=-9\\\\x=\pm 3\quad and\quad x=\pm3i`

`b)\ x^4+10x^2+25=0\\\\(x^2+5)^2=0\\\\x^2=-5\\\\x=\pm i\sqrt5`

`c)\ x^4-x^2-6=0\\\\(x^2-3)(x^2+2)=0\\\\x^2-3=0\quad and\quad x^2+2=0\\\\x^2=3\qquad and\quad x^2=-2\\\\x=\pm\sqrt3\quad and\quad x=\pm i\sqrt2`