Solve by Factoring x^4-7x^2+12=0

Problem

x4−7*x2+12=0

Solution

1. Identify the equation as a trinomial in quadratic form by letting u=x2 which transforms the equation into u2−7*u+12=0

2. Find two numbers that multiply to 12 and add to −7 which are −3 and −4

3. Factor the trinomial into two binomials using these values.

(x2−3)*(x2−4)=0

4. Factor the difference of squares x2−4 into (x−2)*(x+2)

(x2−3)*(x−2)*(x+2)=0

5. Set each factor equal to zero to solve for x

x2−3=0⇒x2=3⇒x=±√(,3)

x−2=0⇒x=2

x+2=0⇒x=−2

Final Answer

x4−7*x2+12=0⇒x=√(,3),−√(,3),2,−2

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