Question:
What should be added to the polynomial $x^{2}-5 x+4$, so that 3 is the zero of the resulting polynomial?
(a) 1
(b) 2
(c) 4
(d) 5
Solution:
If $x=\alpha$, is a zero of a polynomial then $x-\alpha$ is a factor of $f(x)$
Since 3 is the zero of the polynomial $f(x)=x^{2}-5 x+4$,
Therefore $x-3$ is a factor of $f(x)$
Now, we divide $f(x)=x^{2}-5 x+4$ by $(x-3)$ we get
Therefore we should add 2 to the given polynomial
Hence, the correct choice is $(b)$
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