Question

Find the polynomial function with leading coefficient -7; degree 3; and 4, 1/4, and 5/4 as zeros.

Answer 1

So if some number is a zero of a polynomial, then (x-number) is a factor of that function. So when we try to find these, we set it up like this:
\[a(x-c _{1})(x-c _{2})(x -c_{3})\]Because this is degree 3, that means we have 3 factors.The a is an unknown constant. We put it there so we can find a way to get that -7 we need. We may have to multiply what we get by some number to get what we want. Those c values are the zeros we're given. So finally we can put this:
\[a[(x-4)(x-\frac{ 1 }{ 4 })(x-\frac{ 5 }{ 4 })]\]
Now what we need to do is multiply this out and see what we get. Don't multiply in the a, leave that out. Think you can do that?

Answer 2

16x^3-88x^2+101x-20

Answer 3

Not bad xD So now we have that random a out in front. So we need that a to be some number that when multiplied by 16 makes -7.

Answer 4

-7/16

Answer 5

F(x)=-7x^3+(77/2)x^2-(707/16)x+35/4

Answer 6

There ya go :P I was just looking to see if I could find a way to get ridof the fractions and still keep the coefficient -7 xD But thats what I got :P