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2 years ago

HELP ME PLEASE!!!!!!!!!!4(a+2)=8+4a

Mathematics

2 answers:

user100 [1]2 years ago

4 0

All real numbers are correct! Hope that helps.

Natasha2012 [34]2 years ago

4 0

Answer:

a can be anything. There are infinite solutions.

Step-by-step explanation:

$4(a+2)=8+4a$

Expand:

$4a+4\times\:2=8+4a$

$4a+8=8+4a$

Subtract 8 from both sides:

$4a+8-8=8+4a-8$

$4a=4a$

Subtract 4a from both sides:

$4a-4a=4a-4a$

$0=0$

Since both sides are equal, a has infinite solutions as no matter what value it is, it will not affect the end result of $0=0$ which is true.

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2 years ago

Find all the zeros of the equation x^4-6x^2-7x-6=0

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Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

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Again factor using the rational root test, we get

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

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

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$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

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