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Write a quadratic equation with integer coefficients for each pair of roots.$3+i, 3-i$
$x^{2}-6 x+10=0$
Algebra
Chapter 5
QUADRATIC FUNCTIONS AND COMPLEX NUMBERS
Section 7
Sum and Product of the Roots of a Quadratic Equation
Equations and Inequalities
Quadratic Functions
Complex Numbers
Polynomials
Missouri State University
McMaster University
Idaho State University
Lectures
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Write a quadratic equation…
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A polynomial equation with…
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we have a root equal to three plus I and another one You put a three minus I. And so this is actually, although it might look complex of lots gonna cancel out. For instance, when I add these 23 plus I and three minus I, you can see the eyes were gonna cancel out right away. And this is equal to negative. Be over a which whenever you can make a equal one, life will be easier. And so, like I said, we have a positive I in a negative I that cancel out three plus three is equal to six, and so six is equal to negative B if I must, by both sides of the negative one. B is equal to negative six. Now over here, let's find a product. Let's do three plus I and multiply it by three minus. I equal to see over a and remember is equal to one. So three times three is nine we got I times three as a positive three i in a negative items story and negative. Three of those will cancel and then we have I times a negative I Well, im times eyes negative one right, Remember, that's what we know about I squared equals negative one and so a negative I squared is a positive one equal to see over one. Well, that's see. So nine plus one is 10. There's RC Die. We can write the cigarette quadratic equation using a is one So x squared B is negative six So neg 06 x and a C of 10 senate equals zero rather.
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