Answer:
x= 0.0000 - 8.6603
x= 0.0000 + 8.6603
Step-by-step explanation:
Step 1 :
Polynomial Roots Calculator :
1.1 Find roots (zeroes) of : F(x) = x2+75
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 75.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,5 ,15 ,25 ,75
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 76.00
-3 1 -3.00 84.00
-5 1 -5.00 100.00
-15 1 -15.00 300.00
-25 1 -25.00 700.00
-75 1 -75.00 5700.00
1 1 1.00 76.00
3 1 3.00 84.00
5 1 5.00 100.00
15 1 15.00 300.00
25 1 25.00 700.00
75 1 75.00 5700.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step 1 :
x2 + 75 = 0
Step 2 :
Solving a Single Variable Equation :
2.1 Solve : x2+75 = 0
Subtract 75 from both sides of the equation :
x2 = -75
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -75
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Accordingly, √ -75 =
√ -1• 75 =
√ -1 •√ 75 =
i • √ 75
Can √ 75 be simplified ?
Yes! The prime factorization of 75 is
3•5•5
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).
√ 75 = √ 3•5•5 =
± 5 • √ 3
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x= 0.0000 + 8.6603 i
x= 0.0000 - 8.6603 i
Two solutions were found :
x= 0.0000 - 8.6603 i
x= 0.0000 + 8.6603 i
Processing ends successfully
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