Question

If x2−7x+10=0 and x2−5x+c=0 have a common root, then find the value of c​

Answer 1

Step-by-step explanation:

${x}^{2} - 7x + 10 = 0 \\ {x}^{2} - 5x - 2x + 10 = 0 \\ x(x - 5) - 2(x - 5) = 0 \\ (x - 5)(x - 2) = 0 \\ roots \: are \: = 5 \: and \: 2 \\ \\ putting \: the \: value \: of \:5 \: and \: 2\: in \: {eq}^{n} \: {2}^{nd} \\ \\ {x}^{2} - 5x + c \: = 0 \\ for \: 5 \\ {5}^{2} - 5 \times 5 + c \: = 0 \\ 25 - 25 + c \: = 0 \\ c \: = 0 \\ \\ for \: 2 \\ \\ {2}^{2} - 5 \times 2 + c = 0 \\ 4 - 10 + c = 0 \\ - 6 + c = 0 \\ c \: = \frac{0}{ - 6} \\ c \: = 0$

Hence, the value of c = 0