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# ​ What are the roots of the equation?

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What are the roots of the equation? Jan 27, 2018

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New Year, New Start, New Answer!

First answer of the year for me.

Alright, I'll try to explain this the best I can using a keyboard. The equation is x^2(6x - 11)(7x - 8) = 0

So, you have to figure out what you can put in for x for the whole thing to equal 0.

Roots mean possible solutions.

Let's "divide" the equation into 3 parts.

We know that anything multiplied by 0 is 0.

And 0 to the power of anything is still 0.

So if you plug in 0 for x^2(6x - 11)(7x - 8) = 0, You get 0 (it would look like "0(6x-11)(7x-8)" )

So the first root is 0.

Next, let's look at the (6x - 11) part.

Remember that anything multiplied by 0 is 0.

So, 6x - 11 must equal to 0.

6x-11=0

6x=11

x=11/6

So another root is 11/6.

Finally, let's look at (7x-8)

That should also equal 0, no matter what it is multiplied by.

7x-8=0

7x=8

x=8/7

The last root is 8/7

So the three roots are 0, 11/6, and 8/7.

Jan 27, 2018