Roots vs Solutions

I have a doubt regarding the definitions of both.
The example I had in a question was $(x-2)^3 (x-3)=0$ has how many solutions?

According to me it has 4 roots but 2 solutions while my instructor disagrees and says it has 4 roots and 4 solutions. So, which is correct?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Both of you are wrong because there is no equation.

Pi Han Goh - 4 years ago

Well; sorry!! I forgot about the zero. Now, who is correct?

Yatin Khanna - 4 years ago

Both are correct. For clarity, we should specify that there are 4 solutions, 3 of which are equal.

Pi Han Goh - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$