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

if the roots of the equationsgiven in the picture as question no 3 are simultaneously real then prove that b2ac class=

Respuesta :

caylus
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

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