Question

For what value of k, is –3 a zero of the polynomial x² + 11x + k?

Answer 1

We know that if x = a is zeros polynomial, 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) = x^2 + 11x + k`  by  `g(x)= x+3` to find the value of k.

                     x + 8
`x + 3")"overline(+ \cancel(x^2) + 11x + k)`
          `+ \cancel(x^2) + 3x`
           –        –      
                  `+ \cancel(8x) + k`
                  `+ \cancel(8x)       +24`
                   –            –      
                              k – 24

Now, Remainder = 0 

`k - 24 = 0`

`k = 24`

Hence, the value of k is 24.