Answered

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The quadratic function g(x)=ax^2+bx+c has the complex roots (10+i) and (10-i). You may assume that a=1.
What is the value of b?
What is the value of c?

Sagot :

batolisis

The values are [tex]b=-20\text{ and }c=101[/tex]

The quadratic function, expressed in factored form is

[tex](x-(10+i))(x-(10-i))=g(x)[/tex]

Expanding and simplifying

[tex]g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101[/tex]

since

[tex]g(x)=ax^2+bx+c=x^2-20x+101[/tex]

we can equate coefficients of like-terms and conclude that

[tex]a=1,b=-20,c=101[/tex]

Learn more about quadratic equations here: https://brainly.com/question/12995618

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