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