What is the quadratic equation that has the roots 3+i and 3−i ?(1 point) Responses x^2−6x+8=0 x squared minus 6 x plus 8 equals 0 x^2+6x−10=0 x squared plus 6 x minus 10 equals 0 x^2−6x+10=0 x squared minus 6 x plus 10 equals 0 x^2+6x+10=0
To find the quadratic equation with the given roots, we can use the fact that if a quadratic equation has roots α and β, then the equation can be written as (x - α)(x - β) = 0.
In this case, the roots are 3+i and 3-i. Plugging in these values, we get:
(x - (3+i))(x - (3-i)) = 0
To simplify this expression, we expand it:
(x - 3 - i)(x - 3 + i) = 0
Using the distributive property, we have:
(x - 3)^2 - (i)^2 = 0
Simplifying further, we have:
(x - 3)^2 - i^2 = 0
(x - 3)^2 - (-1) = 0
(x - 3)^2 + 1 = 0
This is the quadratic equation with the given roots. So the correct answer is:
x^2 - 6x + 10 = 0