How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 0, 2, 2, 4?

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Answer 1 · 2016-09-12T04:28:30

#x^4-8x^3+20x^2-16x=0#

We'll start with the zeros:

#x=0, x=2, x=2, x=4#

These are called "zeros" because we're looking for where the graph crosses the X-axis - or in other words, where "y=0". So we'll have:

#x=0, x-2=0, x-2=0, x-4=0#

We do this because in a function, if one term within an equation that is all multiplication equals 0, the entire function equals 0. So we get:

#x(x-2)(x-2)(x-4)=0#

And now it's just expanding all these terms into one polynomial equation:

#x(x^2-4x+4)(x-4)=0#

#x(x^3-8x^2+20x-16)=0#

#x^4-8x^3+20x^2-16x=0#