Question

5. Is it possible for a quadratic function to have one real zero and one imaginary zero? Why or why not?

Answer 1

As you use the next formula o get the zeros in a quadratic function:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

The possiblitity to have a imaginary zero is that ther part:

$b^2-4ac<0$

If that part is negative, then both zeros are imaginary because the square root of a negative number is a imaginary number and any real number add to an imaginary number is a complex number (a +bi, i is imaginary unit)

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$b^2-4ac>0$

If that part is possitive both zeros are real numbers

Then, is not posible for a quadratic function to have one real zero and one imaginary zero. Because both zeros are real or both zeros are imaginary.