Question

find the value of k for which one root of the quadratic equation x2-7x+k=0 is six times the other

Answer 1

let alpha and beta be the zeros of the given polynomial

ATQ

1st root=alpha

2nd root / beta=6alpha

alpha+beta=-b/a

alpha+6alpha=7/1

7alpha=7

alpha=1

alpha * beta = c/a

alpha * 6 alpha= k

6alpha ^2=k        (as alpha=1)

6(1)^2=2

6=k