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2 years ago

PLEASE HELP ME SOMEONE UGH I HATE WORK IM SO BAD :(

Mathematics

2 answers:

ivann1987 [24]2 years ago

8 0

Answer:

see the answer above by picture. i think i helped mark me as brainlist plz

kipiarov [429]2 years ago

7 0

Answer:

X=19/3

Step-by-step explanation:

3x=14+5

3x=19

X=19/3

and I feel you hegarty can be a pain in the a.ss

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

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Option 1 is correct.

Step-by-step explanation:

The given polynomial is

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

we have to find all the rational roots of the polynomial f(x)

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of $\frac{p}{q}$

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.

$\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12$

$\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$

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

$\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}$

Now, the rational roots of polynomial satisfy the given polynomial

$f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12$