Question

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

Answer 1

The values are $b=-20\text{ and }c=101$

The quadratic function, expressed in factored form is

$(x-(10+i))(x-(10-i))=g(x)$

Expanding and simplifying

$g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101$

since

$g(x)=ax^2+bx+c=x^2-20x+101$

we can equate coefficients of like-terms and conclude that

$a=1,b=-20,c=101$

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