Question

find the value of a and b.if x+1 and x-5 are the factors of x3-3x2-ax+b.How to do?

Answer 1

$\textit{ \textbf{ Hello Mate! }}$

By factor theorum we know that p(x).

Here, x = - 1 , 5 [ Factors were, ( x + 1 ) ; ( x - 5 )

$p(x) = {x}^{3} - 3 {x}^{2} - ax + b \\ p( - 1) = {( - 1)}^{ 3} - 3 {( - 1)}^{2} - a( - 1) + b \\ 0 = - 1 - 3 + a + b \\ 4 = a + b.......(1) \\ \\ p( 5) = {5}^{3} - 3 ({5}^{2} ) - a(5) + b \\ 0 = 125 - 75 - 5a + b \\ 50 = 5a - b.......(2) \:$

On adding both equation we get

$54 = 6a \\ 9 = a$

Keeping value of a in eqn (1)

$4 = 9 + b \\ - 5 = b$

$\boxed{ \textsf{ Hence,\:value\:of\:a\:=9\:and\:b=-5 }}$

$\texttt{ Have great future ahead! }$