Question

the common root of x2-5x+6=0 and x2-x-2=0​

Answer 1

2. x^2_x_2

x^2_2x+x_2

x(x_2)+1(x_2).

(x_2)(x+1).

Answer 2

Answer:

=common root in both the eqn is 2 ✔✔

Step-by-step explanation:

${x}^{2} - 5x + 6 = 0 \\ middle \: term \: splitting \\ {x}^{2} - 2x - 3x + 6 = 0 \\ x(x - 2) - 3(x - 2) = 0 \\( x - 3)(x - 2) = 0 \\ x = 3 \: and \: 2 \\ second \: eqn \\ {x}^{2} - x - 2 = 0 \\ d = {b}^{2} - 4ac \\ \: \: \: = ({ - 1})^{2} + 8 \\ \: \: \: = 1 + 8 = 9 \\ x = \frac{ - b + \sqrt{d} }{2 \times a } \: \: \: \: \: \: \: \: \: \:\frac{ - b - \sqrt{d} }{2 \times a } \\ \: \: \: \:= \frac{1 + 3}{2} \: \: \: \: \: \: \: \: \: \: \: \frac{1 - 3}{2} \\ \: \: \: = \frac{4}{2} \: \: \: \: \: \: \: \: \: \: \frac{ - 2}{2} \\ x = 2 \: and \: - 1 \\ common \: roots \: between \: both \: the \: eqn \: are \: \\ = 2 \\ so \: answer \: is \: 2$