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3 years ago

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 2

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 2

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3 years ago

Someone help please!!!

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Answer:

y intercept = -5 

slope= 4 

equation: y = 4x - 5

EXPLANATION:

FIRST, you must write the formula for a linear graph , which is y = m(x) + c

where y is any y component and x is it's corresponding x component , m is the gradient or slope and c is the constant or y intercept.

SOLUTION:

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=( (-1)-(-5) ) ÷ (1-0)

= -1+5 ÷ 1

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Therefore, the slope is 4

finding the y intercept.

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in the above equation, I substituted the value I had for the slope or the gradient or m.

SO NOW IM ABOUT TO FIND C

TO FIND C, YOU MUST FIRST PICK A CORRESPONDING Y AND X COMPONENT.

I CHOOSE MY Y = 3 and X = 2

Now I'm going to substitute those values into the formula.

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since it's an equation with one variable, no need for simultaneous equations.

3 = 8 + c

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SO THATS HOW WE ARRIVED AT -5 AND 4.

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I HOPE IT WAS HELPFUL.

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3 years ago

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