SOLUTION: Solve the equation x^4-13x^2+30? List all real solutions, separated by commas? x=

Algebra.Com
Question 1136757: Solve the equation x^4-13x^2+30?
List all real solutions, separated by commas?
x=
Found 3 solutions by Boreal, Alan3354, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!

this factors into an x^2- and an x^2- because the middle term is negative and last term is positive. One can use a u substitution where u=x^2
(u-10)(u+3)=0 The given is an expression, the equal sign 0 makes it an equation.
u=10 and -3
x^2=10
x+=/- sqrt (10) or (-sqrt(10), + sqrt (10)) ANSWER.
The other two solutions are complex/imaginary
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
That is not an equation.
Equations have equal signs.
---
x^4-13x^2+30 = 1 is an equation.
x^4-13x^2+30 = 5 is an equation.
x^4-13x^2+30 = 100 is an equation.
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

            First,  it is not an equation,  since it has no right side and the equality sign.

            So,  we can talk about a polynomial,  but not about equation.

            And the question,  if to formulate it correctly,  should be  THIS : 

                Find the roots of this polynomial.

            Second, the solution and the answer by @Boreal both are incorrect, since his factoring is incorrect.

            Below find the correct solution. 


Introduce new variable  u = x^2.

Then your polynomial takes the form


    u^2 - 13u + 30


It can be factored in this way


    u^2 - 13u + 30 = (u-3)*(u-10) 


so, it has the roots  u = 3  and  u = 10, both positive.


It means, that the original polynomial has 4 (four) real roots  , ,    and  .    ANSWER

Solved.


RELATED QUESTIONS

solve the equation x^4-13x^2+30=0. list the real solutions separated by... (answered by ikleyn)
Find all solutions of the equation. (Enter all answers including repetitions. Enter your... (answered by Alan3354,ikleyn,Edwin McCravy)
Find all real numbers x that satisfy the equation |x + 4| + |x - 7| = 3x - 1 + |3x - 7|. (answered by CPhill,josgarithmetic)
Find all EXACT solutions of the equation cos(x ) = −1/2 in the interval... (answered by Edwin McCravy)
solve 4 sin(pi/4 x)=2 for the four smallest positive solutions x= give answers... (answered by MathLover1)
Find all solutions of the equation e^x − 30 e^(−x) = −7 If there... (answered by josmiceli)
Find all values of x such that \frac{2x}{x + 2} = \frac{x - 3}{x - 4} + \frac{2x + 7}{x... (answered by yurtman)
Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find... (answered by Fombitz)
The function f(x) is defined for 1 <= x <= 5 as follows: f(x) = 2x + 1 if 1 <= x... (answered by stanbon)