Question

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

Answer 1

Since a and b are the zeros of the polynomial $f\left(x\right)=x^2-5x+k$

The standard quadratic equation is $p{x}^2+qx+r=0$

Then Sum of roots = $-\frac{q}{p}$

and Product of roots = $\frac{r}{p}$

Therefore,

$a+b=5$ and $ab=k$

Now, $a-b=1$

$(a-b{)}^2=1$

$(a+b{)}^2-4ab=1$

$25-4k=1$

$24=4k$

$k=6$