Question

Find all rational zeros of the polynomial
P(x)= 2 x^4 + 1 x^3 - 4 x^2 + 1 x - 6

I have tried this problem 28 times and have only been able to come up with one of the zeros, which is -2

Answer 1

The Rational Root Theorem (RRT) states that if there are rational roots, they must be of the form: p/q, where p is a divider of the constant term, and q is a divider of the first coefficient.

Dividers of constant term (-6) are: 1, -1, 2, -2, 3, -3, 6, -6
Dividers of first coeff. (2) are: 1, -1, 2, -2.

So possible rational roots are: \[\pm \frac{ 1, 2,3,6 }{ 1,2 }\]or if you simplify these possible numbers:\[\pm1,\pm2,\pm \frac{ 3 }{ 2 },\pm3,\pm6\]That narrows down the search...

Answer 2

The attached plot should help, like x=1.5?

Answer 3

I actually had tried all of those numbers and only came out with -2

Answer 4

Thank you. i'll try that point in my synthetic division

Answer 5

\[\frac{2 x^4+x^3-4 x^2+x-6}{x-\frac{3}{2}}=2 x^3+4 x^2+2 x+4 \]

Answer 6

thank you.

Answer 7

Thank you for the medal and you're welcome.