Question

find the value of p if px(x-3)+9=0 has equal roots

Answer 1

$px(x - 3) + 9 = 0 \\ p {x}^{2} - 3px + 9 = 0$
...
methods::===
(1).for an equation to have equal roots... discriminant of equation should equal to zero

(2).make it perfect square and put zero....

first one is easy...

$d = ( - 3p) {}^{2} - 4(p)(9) = 0 \\ 9 {p}^{2} = 36p \\ {p}^{2} = 4p \\ p = 0 \: or \: 4$


p can't equal to zero.. as equation will not remain quadratic any longer hence p =4


p=4..

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