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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.  

  1. Mercedes says, “Just remember when we made factors from the roots. If the roots are and the equation is .” Use Mercedes’s idea to help Phyllis write the equation of a quadratic function.

    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.

  2. Darin says, “No, no, no. You can do it that way, but that’s too complicated. I think you just start with and work backwards. So , then, square both sides… Yeah, that’ll work.” Try Darin’s method.

  3. Whose method do you think Phyllis should use? Explain your choice.