Question

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

Answer 1

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

Since 3 is zero of f(x)

Therefore x – 3 is a factor of  f(x)

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

                    2x + 7
`x - 3")"overline(+ \cancel(2x^2) + x + k)`
           `+ \cancel(2x^2) - 6x`
           –           +        
                     `+ \cancel(7x) + k`
                     `+ \cancel(7x)         -21`
                     –                +      
                                k + 21

Now, remainder = 0

`k + 21 = 0 `

` k = -21`

Hence, the value of k is = –21.