Question

find the value of P for which Quadratic equation x^2+4px+p+2=0 has equal and real roots​

Answer 1

Answer:

$p = \frac{1 + \sqrt{33} }{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: p = \frac{1 - \sqrt{33} }{8} .$

Step-by-step explanation:

${x}^{2} + 4px + p + 2 = 0 \\ \\ 16 {p}^{2} - 4(p + 2) = 0 \\ \\ 4 {p}^{2} - p - 2 = 0 \\ \\ p = \frac{ - ( - 1) + \sqrt{1 + 32} }{2 \times 4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: p = \frac{ - ( - 1) + \sqrt{1 + 32} }{2 \times 4} \\ \\ p = \frac{1 + \sqrt{33} }{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: p = \frac{1 - \sqrt{33} }{8} .$