Week 4 - 'Repeated' Root - Doubt

[Zohair Merchant]

Hi all,

In the lecture L4.4 and AQ4.4 Question 3, the term 'repeated' roots have been told.

For example in AQ4.4 Question 3, We find the vertex at the x-intercept (3,0) so 3 will be the root. 

Doubt:

Why they have told 'repeated' root? Meaning 3 and 3. Why not just 3? How is it 'repeated' root?

Similarly, How is it 'repeated' root -1 and -1 in the lecture L4.4? Why the word 'repeated' ?

Regards, Zohair.

[Anand Iyer]

quadratic equations typically have two roots.  

It's just incidental that both roots are same in these cases.  In such case, it's customary to say that the roots are repeated.

Thus, (x + 2)^2 has a repeated root -2.  It just means, both roots are equal to -2.  

If you plot the graph of this equation, you'll notice that it touches the X-axis at the root (-2).  Note that this is the same as the vertex if you use the formula -b/2a on the expanded function x^2 + 4x + 4.

[Zohair Merchant]

The vertex's x-coordinate is the only point where we get the x-intercept. So what's the second condition where we get the same x-intercept. Why the word 'repeated' when we found the x-intercept at only one situation which is the vertex's x-coordinate?

Do we say the root is repeated just because there are supposed to be 2 roots but in this case there's only 1, so just for the sake of it, or is there a mathematical reason behind the word 'repeated'?

Regards,

Zohair

[DHARMA TEJA GODUMALA]

what anand explained above is correct.

For quadratic equation you will have two roots , if two roots are same then it is repeating twice so it is repeated root.