SOLUTION: Find the quadratic equation in x with the given roots 1±3i√5 / 2 <- (it is a fraction). Show clear solution thanksss!

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Question 1172153: Find the quadratic equation in x with the given roots 1±3i√5 / 2 <- (it is a fraction). Show clear solution thanksss!
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Use the zero product property to help go from the given roots to a quadratic polynomial.

or

or Multiply both sides by 2

or Subtract 1 from both sides

or Square both sides



Use i^2 = -1





FOIL







This is the final answer.

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We can use the quadratic formula to confirm this

For , we have a = 2, b = -2, c = 23

or

or

or

or

or

or

or

or

We end up with the roots that were given to us. So this confirms that has the proper roots we were given. In other words, this confirms that the given roots lead to

Note: we could scale both sides of by some nonzero number k, and get the same roots (since we can undo this and divide both sides by k). To keep things fairly simple, we'll make k = 1. We can consider to be reduced as much as possible since the coefficients 2,-2,23 only have the common factor 1 between them.

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Answer:



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the quadratic equation in x with the given roots 1±3i√5 / 2 <- (it is a fraction). Show clear solution thanksss!
 ====> 

As seen above, and based on the quadratic equation formula, 1 = - b___b = - 1

Also, as seen above, and based on the quadratic equation formula, 

                                                                  

Finally, as seen above, and based on the quadratic equation formula, the DISCRIMINANT, 

                                                                  

                                                                   <====== General form of a quadratic equation

                                                                   -------- Substituting 1 for a, - 1 for b, and  for c.

                                                                   ----- Multiplying the above by LCD, 2 

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