Question

If the quadratic equation `px^2-2sqrt5px+15=0`  has two equal roots then find the value of p.  

Answer 1

It is given that the quadratic equation `px^2-2sqrt5px+15=0` has two equal roots. 

∴`D=0` 

⇒`(-2sqrt5p)^2-4xxpxx15=0` 

⇒`20p^2-60p=0` 

⇒` 20p(p-3)=0` 

⇒`p=0  or  p-3=0` 

⇒`p=0  or p=3` 

For `p=0`, we get `15=0` which is not true. 

∴`p≠0` 

Hence, the value of p is 3.