Question

if the roots of the equations(given in the picture as question no. 3) are simultaneously real then prove that b2=ac

Answer 1

Hi,
1) ax²+2bx+c=0 have real roots then (2b)²-4ac>=0 ==> 4b²>=4ac ==> b²>=ac
2) bx²-2√(ac)x+b=0 have real roots then
(-2√(ac))²-4b²>=0==> 4ac>=4b²==> ac>=b²
So b²>=ac>=b²==> b²=ac