Question

find a and b,if x-1 and x-2 are factors of the polynomial x3-10x2+ax+b

Answer 1

I hope it helpful to you

Answer 2

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

f ( x ) = x - 1 and g ( x ) = x - 2 are factors of p ( x ) = $x^{3} - 10x^{2} + ax + b$

Divide p ( x ) by f ( x ):-

x - 1 = 0

=》 $\boxed{x = 1}$

=》 $1^{3} - 10(1)^{2} + a(1) + b$ = 0
=》 1 - 10 + a + b = 0
=》 a + b = 9

=》 $\boxed{b = 9 - a}$ ...(1)

Divide p ( x ) by g ( x ):-

x - 2 = 0

=》 $\boxed{x = 2}$

=》 $2^{3} - 10(2)^{2} + a(2) + b$ = 0
=》 8 - 40 + 2a + b = 0
=》 2a + b = 32

=》 $\boxed{b = 32 - 2a}$ ....(2)

(1) = (2)

=》 b = b
=》 9 - a = 32 - 2a
=》 - a + 2a = 32 - 9
=》 a = 32 - 9

=》 $\boxed{a = 23}$

=》 b = 9 - a

=》 $\boxed{b = ( -14)}$