Question

If 2 is a root of the equation x^2+bx+12=0 and the equation x^2+bx+q=0 has equal roots,then q=

Answer 1

Step-by-step explanation:

$If \: 2 \: is \: the \: root \: of \: {x }^{2} \: + bx + 12 = 0 \\ then \: it \: satisfy \: the \: equation \\ {2}^{2} + 2b + 12 = 0 \\ 4 + 12 + 2b = 0 \\ 2b = - 16 \\ b = - 8 \\ then \: putting \: the \: value \: of \: b \: in \: second \: equation \\ {x}^{2} - 8x + q = 0 \\ that \: equation \: has \: equal \: roots \\ then \: {b}^{2} - 4ac = 0 \\ \: \: \: \: \: \: \: = 64 - 4q = 0 \\ \: \: \: \: \: \: \: = 4q = 64 \\ \: \: \: \: \: \: \: = q \: = 16$

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