Question

if a=x+20 and b=x+1 find the value of a and b where a and b are perfect squares

Answer 1

Given a and b are roots of the equation x^2+ax+b=0.
Sum of the roots a+b=-a.........(1)
Product of the roots ab=b.......(2)
(1)=>2a+b=0 and (2)=>a=1 or b=0.
a=1=>b=-2
Thus we have x^+x-2=0 i.e (x+1/2)^2-9/4=0.
Hence minimum value of x^2+ax+b=0 is -9/4.