Question

If $\alpha$ and $\beta$ are the zeros of the polynomial $p\left(x\right)=x^2-5x+k$ and $\alpha -\beta =1$, then find $k$.

Answer 1

Consider the given polynomial.

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

Since, $\alpha ,\beta$ are the zeroes of given polynomial.

So,

$\alpha +\beta =5$

$\alpha \beta =k$

Since, $\alpha -\beta =1$

Therefore,

$2\alpha =1+5$

$2\alpha =6$

$\alpha =3$

And $\beta =2$

Therefore,

$3\times 2=k$

$k=6$

Hence, this is the answer.