Question

If $\alpha$ and $\beta$ are the zeroes of polynomial $x^2-5x+k$ such that $\alpha -\beta =1$, find $k$

Answer 1

$x^2-5x+k$

Here, a=1, b=-5 and c=k

Now, $\alpha +\beta =-b/a=-(-5)/1=5$

$\alpha \ast \beta =c/a=k/1=k$

Now,α - β =1

Squaring both sides, we get,

$(\alpha -\beta {)}^2=1^2$

$\Rightarrow (\alpha +\beta {)}^2-4\alpha \beta =1$

$\Rightarrow (5{)}^2-4k=1$

$\Rightarrow -4k=7-25$

$\Rightarrow -4k=-24$

$\Rightarrow k=6$ So the value of k is 6.