Questions: What is the quadratic equation that has the roots 3+i and 3-i? (1 point) - (x^2+6 x-10=0) - (x^2-6 x+8=0) - (x^2-6 x+10=0) - (x^2+6 x+10=0)

Solution Steps

To find the quadratic equation with given roots, we use the fact that if \( p \) and \( q \) are the roots of a quadratic equation, then the equation can be expressed as \( (x - p)(x - q) = 0 \). Here, the roots are \( 3+i \) and \( 3-i \). We can expand the expression \( (x - (3+i))(x - (3-i)) \) to find the quadratic equation.

The given roots of the quadratic equation are \( 3+i \) and \( 3-i \).

Using the roots, we can express the quadratic equation as: \[ (x - (3+i))(x - (3-i)) = 0 \]

Expanding the expression: \[ (x - (3+i))(x - (3-i)) = (x - 3 - i)(x - 3 + i) \] This simplifies to: \[ (x - 3)^2 - (i)^2 = (x - 3)^2 + 1 \]

Expanding \( (x - 3)^2 + 1 \): \[ (x^2 - 6x + 9) + 1 = x^2 - 6x + 10 \]

Final Answer