maths

A quadratic equation x^2 + px + q = 0, where p and q are integers, has root 3-2(square root 5). Find the values of p and q

It difficult

Reply 1

tonyiptony

Hmm... in theory (...I think...), there should be infinitely many solutions, because we only know one point on the quadratic. (You need at least two to fix monic quadratics, or the coefficient of the x^2 term is 1) .

But if we only want to find one, a good start is to write down the roots explicitly in terms of p and q (how?).

(edited 9 months ago)

Reply 2

mqb2766

Original post by Ktelesia

A quadratic equation x^2 + px + q = 0, where p and q are integers, has root 3-2(square root 5). Find the values of p and q

It difficult

Using the fact that p and q are integers, either sub that root into the equation and spot what p and q are by equating surds and integers seperately. Or spot what the other root must be (quadratic equation) and expand the factorised form.