Question

if (x+1) and (x-1) are the factors of px³+x² -2x + q then find the value of p and q.. please solve it..

Answer 1

Answer:

Step-by-step explanation:

(x+1) and (x-1) are the factors of the polynomial

X= 1, -1

p(1) = p(1)^3 +(1)^2 -2(1) +q

  0 = p +1 -2 +q

   p+q = 1          - equation 1

p(-1) = p(-1)^3 +(-1)^2 -2(-1) + q

    0 = -p+1+2+q

     p-q = 3          - equation 2

adding equation 1 and 2

2p = 4 => p = 2

substituting p=2 in equation 1

2+q = 1  => q = 1-2    => q = (-1)

Answer 2

Answer:

P = 2and Q = -1

Step-by-step explanation:

Let $f(x) = px^3+x^2-2x+q$

since the function $f(x)$ is divisible by $(x+1)$ and $(x-1)$ so we get x = -1  and  x = 1.

The values of x make the function value to be zero i.e, f(x)=0.

Therefore,

$f(1)=0 =p+1-2+q\\\\f(-1)=0 =-p+1+2+q$,

simplifying above  to get,

$p+q=1 --------( 1 ), \\ \\-p+q=-3------( 2 )$

Rewriting ( 2 ) as p=q+3 and substituting in equation ( 1 ),

$q+3+q=1,\\\\2q+3=1\\\\2q=-2\\\\q=-1$

Substituting the value of q in equation ( 1 ) we get the p-value as p = 2.

Therefore, we get P = 2 and q = -1.