Answer:
Two solutions were found :
x= 0.0000 - 2.0000 i
x= 0.0000 + 2.0000 i
Step-by-step explanation:
Find roots (zeroes) of : F(x) = x2+4
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 4.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-2 1 -2.00 8.00
-4 1 -4.00 20.00
1 1 1.00 5.00
2 1 2.00 8.00
4 1 4.00 20.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step 1 :
x2 + 4 = 0
Solving a Single Variable Equation :
2.1 Solve : x2+4 = 0
Subtract 4 from both sides of the equation :
x2 = -4
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -4
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Accordingly, √ -4 =
√ -1• 4 =
√ -1 •√ 4 =
i • √ 4
Can √ 4 be simplified ?
Yes! The prime factorization of 4 is
2•2
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 4 = √ 2•2 =
± 2 • √ 1 =
± 2
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x= 0.0000 + 2.0000 i
x= 0.0000 - 2.0000 i
Two solutions were found :
x= 0.0000 - 2.0000 i
x= 0.0000 + 2.0000 i
Processing ends successfully
Answer:
x = ± 2i
Step-by-step explanation:
x² + 4 = 0 has no real solutions but has 2 complex solutions
Note that [tex]\sqrt{-1}[/tex] = i
Given
x² + 4 = 0 ( subtract 4 from both sides )
x² = - 4 ( take the square root of both sides )
x = ± [tex]\sqrt{-4}[/tex]
= ± [tex]\sqrt{4(-1)}[/tex]
= ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{-1}[/tex]
= ± 2i
Thus the solutions are x = - 2i or x = 2i
