Find a polynomial with a degree of four and zeroes of: 0,-3,1,4 and the coefficient x^3 must be 4

Thanks!

This post was edited by tommyd323 on Sep 26 2016 10:05pm

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Fill it in

Does not give me a coefficient of 4 on the x^3

could i multiply each integer by 4?

closed, i got it

This post was edited by tommyd323 on Sep 26 2016 10:34pm

Assuming this polynomial:

ax4 + bx3 + cx2 + dx + e = 0

and x1, x1, x3 and x4 are the zeros of this polynomial.

We know this:
x1 + x2 + x3 + x4 = – b/a

x1 * x2 + x1 * x3 + x1 * x4 + x2 * x3 + x2 * x4 + x3 * x4 = c/a

x1 * x2 * x3 + x1 * x2 * x4 + x1 * x3 * x4 + x2 * x3 * x4 = – d/a

x1 * x2 * x3 * x4 = e/a


You said b = 4, so lets find "a":
x1 + x2 + x3 + x4 = – b/a
0 -3 + 1 + 4 = -4/a
a = -2

Now finding "e":
x1 * x2 * x3 * x4 = e/a
0*-3*1*4 = e/-2
e = 0

Then lets finish for "c" and "d":
x1 * x2 + x1 * x3 + x1 * x4 + x2 * x3 + x2 * x4 + x3 * x4 = c/a
0*-3 + 0*1 + 0*4 + -3*1 + -3*4 + 1*4 = c/-2
-3 -12 + 4 = c/-2
c = 22

x1 * x2 * x3 + x1 * x2 * x4 + x1 * x3 * x4 + x2 * x3 * x4 = – d/a
0*-3*1 + 0*-3*4 + -3*1*4 = -d/-2
-12 = d/2
d = -24

So, the polynomial is:

-2x4 + 4x3 + 22x2 -24x = 0