Question

if3x^2-2x+p=0 and 6x^2-17x+12=0 have a common root then p=​

Answer 1

Answer:

$3 {x}^{2} - 2x + p = 0 \\ 6 {x}^{2} - 17x + 12 = 10 \\ the \: factors \: of \: equation \: (2) \\ 6 {x}^{2} - 17x + 12 = \\ sum = 6(12) = ac = 72 \\ product = - 17 = b \\ the \: two \: numbers \: r \: ( - 9) \: and \: (- 8) \\ split \: the \: middle \: term \: = 6 {x}^{2} - 9x - 8x + 12 \\ take \: in \: common \: = 3x(2x - 3) - 4(2x - 3) = (3x - 4)(2x - 3) \\ the \: factors \: are \: 3x - 4 = 0 \\ x = \frac{4}{3} and \: 2x - 3 = 0 \\ x = \frac{3}{2} \\ so \: the \: factors \: are \: \frac{4}{3} and \: \frac{3}{2}$