### Home > PC3 > Chapter 4 > Lesson 4.1.3 > Problem 4-43

Phyllis has a problem. She knows that the roots of a quadratic function are * *and

*, but in order to get credit for the problem she needs to know the equation of the function. She is having a hard time with the complex roots, but luckily, her friends are full of advice.*

Mercedes says,

*“Just remember when we made factors from the roots. If the roots are*Useand the equation is .” Generic rectangle, 2 rows, 2 columns, top edge labeled, x minus quantity, 3 + 4 I, left edge labeled, x, minus quantity, 3 minus 4 i.

Labels added: Interior, top left, x squared, to right, negative x times the quantity, 3 + 4 I, bottom left, negative x times the quantity, 3 minus 4 I, bottom right, quantity, 3 minus 4 I, times the quantity, 3 + 4 I.

Interior labels changed: top left, negative 3 x, minus 4 x I, bottom left, negative 3 x, + 4 x I, bottom right, 25.

Darin says,

*“No, no, no. You can do it that way, but that’s too complicated. I think you just start with*Try Darin’s method.and work backwards. So , then, square both sides… Yeah, that’ll work.” Whose method do you think Phyllis should use? Explain your choice.