Solve the quadratic equation x^2-ix+6=0
Answers
Answer:
Simplifying
x2 + ix + 6 = 0
Reorder the terms:
6 + ix + x2 = 0
Solving
6 + ix + x2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + ix + -6 + x2 = 0 + -6
Reorder the terms:
6 + -6 + ix + x2 = 0 + -6
Combine like terms: 6 + -6 = 0
0 + ix + x2 = 0 + -6
ix + x2 = 0 + -6
Combine like terms: 0 + -6 = -6
ix + x2 = -6
Add '-1x2' to each side of the equation.
ix + x2 + -1x2 = -6 + -1x2
Combine like terms: x2 + -1x2 = 0
ix + 0 = -6 + -1x2
ix = -6 + -1x2
Divide each side by 'x'.
i = -6x-1 + -1x
Simplifying
i = -6x-1 + -1x
Concept:
Quadratic equation is the equation with the degree 2.
For example: x²+5x+1.
Factorization method is the method in which we make the factors of the given equation to find the value of the variable.
i is the imaginary number.
Given:
We are given the quadratic equation:
x²-ix+6=0
Find:
We need to solve the given equation.
Solution:
We will be using the factorization method to solve the equation.
We know that i²=-1.
x²-ix+6=0
=x²-ix-6(-1)=0
=x²-ix-6i²=0
x²-3ix+2ix-6i²=0
x(x-3i)+2(x-3i)=0
(x-3i)(x+2i)=0
By solving this we get the values of x as:
x=3i and x=-2i.
Therefore, by solving the equation x²-ix+6=0, we get the values of x as 3i and -2i.
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