Question

If the quadratic px² - 2 √5px + 15 = 0 has two equal roots then find the value of P.​

Answer 1

Answer:

Step-by-step explanation:

Let x &x be two equal roots.

x+x = 2x = 2_/5p.

X=_/5p

X×X = X^2 = 15÷p

5p^2=15÷p.

P^3 = 3

P = cube root of 3

Answer 2

$\huge\mathbb{SOLUTION:-}$

Given quadratic equation is,

$px {}^{2} - 2 \sqrt{5} px \: + \: 15 = 0$

$Here, \: a = p, \: b = 2 \sqrt{5} p, \: c = 15$

$For \: real \: equal \: roots, \: discriminant = 0$

$\therefore b {}^{2} - 4ac = 0$

$\therefore (2 \sqrt{5}p) {}^{2} - 4p(15) = 0$

$\therefore 20p {}^{2} - 60p = 0$

$\therefore 20p(p - 3) = 0$

$\therefore p = 3 \: or \: p = 0$

$But, \: p = 0 \: is \: not \: possible.$

$\therefore \blue{p = 3}$