Question

x^2-2x(1+3p)-7(3+2p) for two equal roots​

Answer 1

Step-by-step explanation:

For two equal roots , D = 0

${b}^{2} - 4ac = 0 \\ {(1 + 3p)}^{2} - 4 \times 1 \times( - 7)(3 + 2p) \\ 1 + 9 {p}^{2} + 6p + 28(3 + 2p) = 0 \\ 9 {p}^{2} + 6p + 1 + 84 + 56p = 0 \\ 9 {p}^{2} + 62p + 85 = 0 \\ 9 {p}^{2} + 17p + 45p + 85 = 0 \\ p(9p + 17) + 5(9p + 17) = 0 \\( 9p + 17)(p + 5) = 0 \\ 9p + 17 = 0 \\ 9p = - 17 \\ p = \frac{ - 17}{9} \\ p + 5 = 0 \\ p = - 5$