Can you solve the equation X^4-625=0 ? The answer must be in the form a+bi

Just a few extra questions:

  • How do you find the degree measure to plug into trigonometric or nth roots form?
  • How do you find the total number of solutions?

Thank you.

2 Answers
Mark D.
May 10, 2018

If #x^4-625=0# then #x^4=625#
#x=root (4)#625 so #x=5#

Jim G.
May 10, 2018

#x=+-5" or "x=+-5i#

Explanation:

#x^4-625" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=x^2" and "b=25#

#rArr(x^2-25)(x^2+25)=0#

#x^2-25=0rArrx^2=25rArrx=+-5larrcolor(blue)"real roots"#

#x^2+25=0rArrx^2=-25#

#rArrx=+-5ilarrcolor(blue)"complex roots"#

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