Question

find the values of a and if (x-1) (x+2) both are the factors of x^3+(3a+1)x^2+bx-18​

Answer 1

Answer:

$a=3$

Step-by-step explanation:

$f(x)=x^3+(3a+1)x^2+bx-18$

Using the Factor Theorem,

• $f(1)=0$

• $f(-2)=0$

$f(1)=1+3a+1+b-18=3a+b-16$

$f(-2)=-8+12a+4-2b-18=12a-2b-22$

$\left \{ {{3a+b=16} \atop {6a-b=11}} \right.$

∴ $a=3$, $b=7$

$f(x)=x^3+10x^2+7x-18=(x-1)(x+2)(x+9)$