Question

If alpha beta are the roots of the equation x²+kx+12=0,such that α-β=1 then find k

Answer 1

I am representing here alpha by P and beeta by Q.

then
P+Q=-k,

P.Q=12,

but it is given that
(P-Q)=1,

(P-Q)²=1²,

(P+Q)²-4P.Q=1,

so we get,

(-k)²-4×12=1,

k²-48=1,

k²=1+48,

k²=49,

k=7