Question

For what value of k, is –2 a zero of the polynomial 3x² + 4x + 2k?

Answer 1

We know that if x = a is zero polynomial then x – a is a factor of f(x)

Since –2 is a factor of f(x). Therefore x + 2 is a factor of f(x)

Now, we divide `f(x) = 3x^2 + 4x + 2x` by `g(x)=x + 2` to find the value of k

                             3x – 2
`x + 2")"overline(+ \cancel(3x^2) + 4x + 2k)`
          `+ \cancel(3x^2) + 6x`
           –          –       
                  `- \cancel(2x) + 2k`
                 `- \cancel(2x) + 0    -4`
                  +                 +     
                                2k + 4

Now, Remainder = 0

`2k +4=0`

`2k = -4`

`k = (-4)/2`

`k = -2 `

Hence, the value of k is `-2 `.