Question

Which of the following quadratic equations has (X - 5) as a root?
(1) x-1/x = 4
(2) x-1/x = 5
(3) x-5/x = 4
(4) x-5/x = -5​

Answer 1

Step-by-step explanation:

x-5 is the root then put x = 5 then the value of equation is 0

x²-5/x=4 is the answer

= 5²-5/5=4

= 25-5=20

= 20=20

= 20-20

= 0

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Answer 2

Therefore the Quadratic equations which has (X - 5) as a root is option (3) x-5/x = 4

Given:

A Quadratic equation has (X - 5) as a root

To find:

Which Quadratic equations has (X - 5) as a root?

From options

(1) x-1/x = 4  (2) x-1/x = 5  (3) x-5/x = 4  (4) x-5/x = -5​

Solution:

Given (X - 5) is a root of Quadratic equation

Take x - 5 = 0 ⇒ x = 5  

Now find for x = 5 which of the given equation will be satisfied

(1) x-1/x = 4                                           (2) x-1/x = 5

Substitute x = 5                                   Substitute x = 5                                          

⇒  5 - 1/5  = 4                                       ⇒  5 - 1/5  = 5  

⇒  4/5  $\neq$ 4                                           ⇒  4/5  $\neq$ 5    

(3) x-5/x = 4                                          (4) x-5/x = -5​

Substitute x = 5                                    Substitute x = 5                                          

⇒  5 - 5/5  = 4                                       ⇒  5 - 1/5  = -5  

⇒  5 - 1 = 4                                           ⇒  5 -1   $\neq$ - 5    

In given options only option (3) will be satisfied

Therefore the Quadratic equations which has (X - 5) as a root is option (3) x-5/x = 4

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