Suppose that f(x) = x^4 + 7x^2 + 12. Find the values of x such that f(x) = 12

f(x) = 12

=> 12 = x^4 + 7x^2 + 12

=> x^4 + 7x^2 = 0

=>x^2 ( x^2 + 7 ) = 0

=> x = 0 or = +/-sqrt(7) i

f(x) = 12

12 = x^4 + 7x^2 + 12; subtract 12 from both sides
12 - 12 = x^4 + 7x^2 + 12 - 12; simplify
0 = x^4 + 7x^2; factor out x^2
0 = x^2(x^2 + 7); set both factors equal to 0

x^2 = 0; square root each side
√(x^2) = √(0); simplify
x = 0

x^2 + 7 = 0; subtract 7 from both sides
x^2 + 7 - 7 = 0 - 7; simplify
x^2 = -7; square root both sides
√(x^2) = √(-7); simplify
x = +/-i√(7)

Blessings

IF f(x)=12 then 12 = x^4 +7X^2 +12
ie X^4+7x^2 =0 so X^2(X^2+7)=0
giving x=0 orx^2=-7 giving complex root of sqrt(7)