# If a and b are the zeros of the polynomial f(x) =x^2 - 5x + k such that (a - b )=1 find the value of k .

Solution: Since a and b are the zeros of the polynomial

$\\ f(x)= x^2 -5x +k$

$\\\therefore a+b=-(-5/1) \\ ;ab=(k/1)$

Now ,

$\\ a-b=1$

$\\\Rightarrow (a-b)^2=1\\ \\ \Rightarrow (a+b)^2-4ab =1\\ \\ \Rightarrow 25 -4k =1\\ \\\Rightarrow 4k=24\\ \\ \Rightarrow k= 6$

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