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

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

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

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If x is real and the roots of the equation a x^2+b x+c=0 are imaginary, then prove tat a^2x^2+a b x+a c is always positive.

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

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

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