Question

find the value of m and n so that the poly. f(x)= x3 - 6x2 +mx-n is exactly divisible by x-1 and x-2.

Answer 1

Step-by-step explanation:

$x - 1 = 0 \: \: \: \: , \: \: \: \: x - 2 = 0 \\ x = 1\: \: \: \: , \: \: \: \:x = 2 \\ f(x) = {x}^{3} - 6 {x}^{2} + mx - n = 0 \\ f(1) = {(1)}^{3} - 6 {(1)}^{2} + m(1) - n = 0 \\ = 1 - 6 + m - n = 0 \\ = m - n = 5 - (i) \\ f(2) = {(2)}^{3} - 6 {(2)}^{2} + m(2) - n = 0 \\ = 8 - 24 + 2m - n = 0 \\ = 2m - n = 16 - (ii) \\ \blue{\mathfrak{\underline{\large{Subtract \: {eq}^{n} \: (i) \: in \: (ii)}}}:} \\ 2m - n = 16 \\ m - n = 5 \\ - \: \: \: \: + \: \: \: \: - \: \: \: \: \: \: \: \\ - - - - - - - \\ \boxed{m = 11} \\ \blue{\mathfrak{\underline{\large{Put \: the \: value \: in \: {eq}^{n} \: (i)}}}:} \\ 11- n = 5 \\ \boxed{n = 6} \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$