Question

if
$\alpha \beta$
are the zeroes of the polynomial f(x) =
${x}^{2}$
-5x+k such that
$\alpha - \beta = 1$
find the value of k​

Answer 1

Answer:

let alpha =A and beta= B are roots so

A^2-5A+k=0 and B^2-5B+k=0

subtract to each other

A^2-B^2-5(A-B)=0

(A+B)(A-B)-5(A-B)=0

A+B=5....(1)

A-B=1......(2)

2A=6, A=3, so B=2

solve

3^2-5×3+k=0

9-15+k=0

k=6