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If 2-3w is a root, how do i find the roots to2w3 -13w2 +46w -65?...

Question

If 2-3w is a root, how do i find the roots to2w3 -13w2 +46w -65?

if 2-3w is a root, how do i find the roots to 2w3 -13w2 +46w -65?



Answers

One of the roots is given. Find the other root.
$-7 w^{2}+b w-5=0 ;-1$

Okay, so let's recall that we have negative 64. You can write this eyes negative four to the power three. So it's rewrite what we have. So we have the Cube roots of negative four to the power of three. And since we have a non power that's this equal to or inside term, which is and I got a four.

Okay, So it's not that we have an index of sick, so we want to create 64 as a power of six is, we have 2356 So let's right now what we have and I Let's note that we haven't even power, so we get the absolute value of two, which is equal to a chip.

Okay, So it's not that we haven't index of brain, so we want to your negative 64 as a power of three so we can rewrite this as a negative for your power of three. Now, let's plug that in. Okay, Now, let's know though, we have a odd power set up, is you negative? Negative for and that's equal to a four.

Okay. This problem. We're looking for the cube root of 64. So what? This is actually asking us if you think about it geometrically that we have this cube and the volume of this cube is 64. So we're wondering if the cube has the volume of 64. What is the edge? My words for Cuba. Now the edges gonna all be the same. So what are those three edges? We have to multiply the lane times A with times the height to get 64. So we call that the cube root. So what number times itself will give us? Well, give us 64. Well, we could think eight, but eight is just two of them. It's just too eight is a square root of 64. So 8th 2 big. We got to break it down some more. We could think of four. Let's see your four works. So put foreign there four times. Four times forward before times for 16. 16 times four does equal 64. So the cube root of 64 will be four


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