Question

If one root of quadratic equation 2x²-px+q=0 is 2+√3 (p,q € rational numbers), then p/q is equal to

Answer 1

We know irrational roots always exist in pairs,hence one root is (2+√3) and other is (2-√3).
Sum of roots =-(-p)/2=p/2
(2+√3)+(2-√3)=4=p/2
P=8
Product of roots=q/2
(2+√3)(2-√3)=2^2-[√3]^2=4-3=1=q/2
q=2
p/q=8/2=4 Ans.