Question

Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots

Answer 1

Step-by-step explanation:

$px(x - 3) + 9 = 0 \\ p {x}^{2} - 3px + 9 = 0 \\ For \: two \: equal \: roots \\ D = 0 \\ {b}^{2} - 4ac = 0 \\ where \: b = - 3p \: , \: a = p \: and \: c = 9 \\ ({- 3p})^{2} - 4 \times p \times 9 = 0 \\ 9 {p}^{2} - 36p = 0 \\ 9p(p - 4) = 0 \\ p - 4 = \frac{0}{9p} \\ p - 4 = 0 \\ p = 4$