Q1) 214
Q2) x²+x⁴+2=0
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@khushi
Answers
Step-by-step explanation:
x
4
−1=0
⇒ (x
2
)
2
−(1
2
)
2
=0
⇒ (x
2
+1
2
)(x
2
−1
2
)=0
⇒ Now, x
2
+1=0 and x
2
−1=0
⇒ x
2
=−1 and x
2
=1
⇒ x=±
−1
and x=±1
⇒ x=±i and x=±1
∴ The roots are 1,−1,i,−i
Step-by-step explanation:
Step by Step Solution

Step by step solution :
STEP1:Trying to factor by splitting the middle term
1.1 Factoring x4+x2+2
The first term is, x4 its coefficient is 1 .
The middle term is, +x2 its coefficient is 1 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 1 .
-2 + -1 = -3 -1 + -2 = -3 1 + 2 = 3 2 + 1 = 3
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step1:
x4 + x2 + 2 = 0
STEP2:
Solving a Single Variable Equation:
Equations which are reducible to quadratic :
2.1 Solve x4+x2+2 = 0
This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using w , such that w = x2 transforms the equation into :
w2+w+2 = 0
Solving this new equation using the quadratic formula we get two imaginary solutions :
w = -0.5000 ± 1.3229 i
Now that we know the value(s) of w , we can calculate x since x is √ w
Since we are speaking 2nd root, each of the two imaginary solutions of has 2 roots
Tiger finds these roots using de Moivre's Formula
The 2nd roots of -0.500 + 1.323 i are:
x = 0.676 + 0.978 i x = -0.676 -0.978 i 2nd roots of -0.500- 1.323 i :
x = -0.676 + 0.978 i x = 0.676 - 0.978 i
Four solutions were found :
x = 0.676 - 0.978 i
x = -0.676 + 0.978 i
x = -0.676 -0.978 i
x = 0.676 + 0.978 i