How do you write a quadratic equation with two sets of zeros: -2 and 7, 1 and -8?

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Answer 1 · 2017-08-08T21:10:36

It cannot be done with a quadratic but can with a quartic:

#x^4+2x^3-57x^2-58x+112#

A quadratic equation has two zeros counting multiplicity, so it cannot have four zeros.

We could combine two quadratics to get a quartic equation with the four zeros specified.

For example:

#(x+2)(x-7) = x^2-5x-14" "# has zeros #-2# and #7#

#(x-1)(x+8) = x^2+7x-8" "# has zeros #1# and #-8#

So:

#(x^2-5x-14)(x^2+7x-8) = x^4+2x^3-57x^2-58x+112#

Has zeros #-2#, #7#, #1# and #-8#.