Question

if alpha and beta are root of equation ax2 + bx + c = 0 ,then the equation with roots alpha/beta and beta/alpha is

Answer 1

we know that
alpha+beta=-b/a
alpha*beta=c/a
but if new roots we get
alpha/beta+beta/alpha
={alpha^2+bera^2}/alpha*beta
={(alpha+beta)^2-2alpha*beta}/alpha*beta
={(-b/a)^2-2c/a}/c/a
={b^2/a^2-2c/a}/c/a
=(b^2-2ca)/ca
again,alpha/beta*beta/alpha=1
so quadratic equation=x^2-{(b^2-2ca)/ca}x+1
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