f(x)=/ square -6x+k

Question

If sigma and b are the zeroes of the polynomial f(x)=x square -6x+k

Answer 1

f(x)=x²-6x+k=x²-6x+9-9+k=(x-3)²-9+k.

To find the zeroes of f(x), solve (x-3)²-9+k=0 so (x-3)²=9-k. If zeroes are not complex then 9-k≥0.

So k≤9 and x=3±√(9-k) so the zeroes are 3+√(9-k) and 3-√(9-k).