Question

Find the value of A and B so that the polynomial x cube + 10 X square + a x + b has x minus 1 and X + 2 as factors

Answer 1

$\Longrightarrow{\boxed{\bold{Answer:a=7\:and\:b=-18}}}$

$\textbf{\underline{Step-by-step explanation :- }}$

p(x) = x³ + 10x² + ax + b

First factor, x - 1

x = + 1

p(1) = 1³ + 10(1)² + a(1) + b

0 = 1 + 10 + a + b

0 = 11 + a + b __(i)

Second factor is x + 2

x = - 2

p(-2) = -2³ + 10(-2)² + a(-2) + b

0 = - 8 + 40 - 2a + b

0 = 32 - 2a + b __(ii)

By subtracting (ii) from (i)

0 = -21 + 3a

21 = 3a

$\bold{\huge{\underline{7\:=\:a}}}$

Substituting value of a in eq (i)

0 = 11 + 7 + b

$\bold{\huge{\underline{-\:18\:=\:b}}}$