Question

if (x+1) and (x+2) are factors of polynomial
x3+ kx² + hx +6, then find h and k​

Answer 1

Answer:

h=11,k=6

Step-by-step explanation:

Given that (x+1) and (x+2) are the factors of the polynomial p(x)=x³+kx²+hx+6

To find the values of h and k.

x+1=0  and  x+2=0

   x=-1  and      x=-2

p(-1)=(-1)³+k(-1)²+h(-1)+6=0

      =-1+k(1)+(-h)+6=0

      =-1+k-h+6=0

      =k-h+5=0

      =k-h=0-5

      =k-h=-5 →→→→→equation 1

p(-2)=(-2)³+k(-2)²+h(-2)+6=0

       =-8+k(4)+(-2h)+6=0

       =-8+4k-2h+6=0

       =4k-2h-2=0

       =4k-2h=+2 →→→→→equation 2

From the equation 1,

k-h=-5

  k=-5+h →→→→→equation 3

Substitute the value of k in equation 2,

4k-2h=2

4(-5+h)-2h=2

-20+4h-2h=2

     -20+2h=2

             2h=2+20

             2h=22

                h=22/2

                h=11

Substituting the value of h in equation 3,

k=-5+h

k=-5+11

k=6

∴h=11 and k=6

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