Question

if the quartic equation px^2-2√5px+15=0 has equal root find p

Answer 1

I hope this answer would be helpful for you

Answer 2

Answer :

Given quadratic equation is,

px^2 - 2√5px + 15 = 0

Comparing this equation with,
ax^2 + bx + c = 0

We get,
a = p
b = -2√5p
c = 15

So the discriminant,
d = b^2 - 4ac

We know that a quadratic equation has equal roots if,
Discriminant = 0
=> d = 0
=> b^2 - 4ac = 0
=> (-2√5p)^2 - 4(p)(15) = 0
=> (4×5×p^2) - 60p = 0
=> 20p^2 - 60p = 0
=> p^2 - 3p = 0
=> p(p - 3) = 0
=> (p)(p - 3) = 0
=> p = 0 or p = 3

But p = 0 is not possible.

● So the value of p is 3.


●●● Hope It Helps ●●●