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ELEN [110]
3 years ago
9

For the equation 2x 3 - 11x 2 + 12x + 9 = 0,the root 3 has a multiplicity of _____.

Mathematics
2 answers:
OleMash [197]3 years ago
8 0
2x^3 - 11x^2 + 12x + 9
= (x - 3)^2( 2x = 1)

The root 3 has multiplicity of 2.
Reika [66]3 years ago
4 0

Answer:

The multiplicity of 3 is <u>2</u>

Step-by-step explanation:

Use\:the\:rational\:root\:theorem

a_0=9,\:\quad a_n=2

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:9,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2

\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:3,\:9}{1,\:2}

\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-3

=\left(x-3\right)\frac{2x^3-11x^2+12x+9}{x-3}

since, \frac{2x^3-11x^2+12x+9}{x-3}=2x^2-5x-3

\mathrm{Factor}\:2x^2-5x-3:\quad \left(2x+1\right)\left(x-3\right)

=\left(x-3\right)\left(2x+1\right)\left(x-3\right)

=\left(x-3\right)^2\left(2x+1\right)

Therefore, the multiplicity of 3 is <u>2</u>

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