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Can anyone help with this?

 

Find all real numbers k, such that the roots of x^2 - 2kx + 5 = 0 are real.  Enter your answer using interval notation.

 May 3, 2020
 #1
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If the roots  are real.....then the discriminant  is  ≥  0

 

So

 

(2k)^2  - 4(1)(5)  ≥  0

 

4k^2  - 20 ≥  0

 

4k^2  ≥ 20

 

k^2  ≥ 5

 

Which implies  that

 

k ≥ √5        or       k ≤  - √5

 

(-inf , - √5]  U   [ √5, inf )   

 

 

cool cool cool

 May 3, 2020

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