Question

Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

Answer 1

A.) -4/5 and 3/4

Step-by-step explanation:

Answer 2

Answer: The all possible rational roots are
`x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm(1)/(2),\pm(3)/(2),\pm(1)/(4),\pm(3)/(4),\pm(1)/(10),\pm(1)/(5),\pm(3)/(5)\pm(3)/(10),\pm(2)/(5),\pm(6)/(5),\pm(1)/(20),\pm(3)/(20),\pm(4)/(5),\pm(12)/(5)`.

Step-by-step explanation:

The given polynomial is,

`f(x)=20x^4+x^3+8x^2+x-12`

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number,

`x=(p)/(q)`

Where p is a factor of constant term and q is the factor of coefficient of leading term.

In the given polynomial the constant is -12 and the leading coefficient is 20.

All possible factor of -12 are
`\pm1,\pm2,\pm3,\pm4,\pm6,\pm12`.

All possible factor of 20 are
`\pm1,\pm2,\pm4,\pm5,\pm10,\pm20`.

So, the all possible rational roots of the given polynomial are,

`x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm(1)/(2),\pm(3)/(2),\pm(1)/(4),\pm(3)/(4),\pm(1)/(10),\pm(1)/(5),\pm(3)/(5)\pm(3)/(10),\pm(2)/(5),\pm(6)/(5),\pm(1)/(20),\pm(3)/(20),\pm(4)/(5),\pm(12)/(5)`