SOLUTION: Q. If one complex zero of a quadratic equation is 2 + i, what is the quadratic equation in ax^2 + bx + c = 0
thanks, Mike
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Question 5071: Q. If one complex zero of a quadratic equation is 2 + i, what is the quadratic equation in ax^2 + bx + c = 0
thanks, Mike
Found 2 solutions by Earlsdon, ichudov:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Starting with the quadratic formula:
and given that:
we can conclude that:
-b/2a = 2 Assuming that a is a non-zero integer, it must be 1, therefore:
-b/2 = 2
So, a = 1, and b = -4
Now we need to find c. Looking at the radical contents, we can conclude that it is equal to -4.
Why? because = -1 Substituting the values of a and b, we find:
=
= Multiply both sides by 2.
= 2 Square both sides.
16 - 4c = 4(-1) Subtract 16 from both sides.
-4c = -20 Divide both sides by -4
c = 5
Now we can write the quadratic equation whose roots (zeros) are (2 +/- i)
x^2 - 4x + 5 = 0
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
This question assumes that the numbers a, b, c are real number.
Because the roots of the equation are complex, they are of form 2+i and 2-i.
The equation is a trinomial that is a product of two binomials
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