Question

find the quadratic equation whose root are 2 and 3 respectively.

Answer 1

Let the quadratic equation be p(x).
The two roots of p(x) are 2 & 3.
Sum of roots=2+3=5
Product of roots=2×3=6
p(x)=k{x^2-(Sum of roots) x+(Product of roots) }
=k(x^2-5x+6)
=x^2-5x+6(where k=1)