Find the condition if the roots of `a x^2+2b x+c=0a n db x^2-2sqrt(a c )x+b=0` are simultaneously real.

If the roots of the equation ax^(2)+2bx+c=0 and -2sqrt(acx)+b=0 are simultaneously real, then prove that b^(2)=ac

if the roots of (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal then a,b,c are in

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a.a b c b. a+2b+c c. -1 d. 0

a,b,c are rational.Then the roots of (a+b+c)x^(2)2(a+c)x+(a-b+c)=0 are.

If the roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal,then prove that 2b=a+c