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Gekata [30.6K]
3 years ago
7

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

Mathematics
2 answers:
denis23 [38]3 years ago
7 0

Answer:

A.) -4/5 and 3/4

Step-by-step explanation:

Gelneren [198K]3 years ago
4 0

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

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=\frac{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\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}

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