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2 years ago

Find the zeros (roots) of the following equations. f(x) = 2x5 - 9x4 + 12x3 - 12x2 + 10x - 3 = 0

1 answer:

8 0

Hi,
$f(1)=2*1^5-9*1^4+12*1^3-12*1^2+10*1-3\\
=2-9+12-12+10-3\\
=0\\

f(x)=(x-1)(2x^4-7x^3+5x^2-7x+3)\\


g(x)=2x^4-7x^3+5x^2-7x+3\\

g(3)=2*3^4-7*3^3+5*3^2-7*3+3\\
=162-189+45-21+3\\
=0\\

g(x)=(x-3)(2x^3-x^2+2x-1)\\

h(x)=2x^3-x^2+2x-1\\

h( \dfrac{1}{2} )=2* \dfrac{1}{8} - \dfrac{1} {4}+1-1\\
=0\\

h(x)=(2x-1)(x^2+1)\\


f(x)=(x-1)(x-3)(2x-1)(x+i)(x-i)\\


$
Roots are 1,3,0.5,i,-i.

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$\huge\text{Hey there!}$

$\mathsf{\dfrac{9}{10}+\dfrac{7}{15}}$

$\large\textsf{FIRST: FIND the LCD (Lowest Common Denominator) then solve}\\\large\textsf{from there!}$

$\large\textsf{If you have calculated it correctly, you should have came up with \underline{\bf 30}}\\\large\textsf{as your LCD (Lowest Common Denominator).}$

$\mathsf{= \dfrac{9\times3}{10\times3}+ \dfrac{7\times2}{15\times2}}$

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$\mathsf{= \dfrac{27+14}{30}}$

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$\mathsf{= \dfrac{41}{30}}\large\textsf{ which you could convert to }\mathsf{1 \dfrac{11}{30}}$

$\boxed{\boxed{\large\textsf{ANSWER: }\bf \dfrac{41}{30} \large\textsf{ or }\mathsf{\bf 1 \dfrac{11}{30}\large\textsf{ because they both equal the same thing}}}}}\huge\checkmark$

$\large\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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