If `a , b , c ,` are real number such that `a c!=0,` then show that at least one of the equations `a x^2+b x+c=0` and `-a x^2+b x+c=0` has real roots.

If a,b,c, are real number such that ac!=0 , then show that at least one of the equations ax^(2)+bx+c=0 and -ax^(2)+bx+c=0 has real roots.

If a,b,c are positive real numbers.then the number of real roots of the equation ax^(2)+b|x|+c=0 is

If a,b,c are positive real numbers,then the number of real roots of the equation ax^(2)+b|x|+c is

If a

Let a,b,c , d ar positive real number such that a/b ne c/d, then the roots of the equation: (a^(2) +b^(2)) x ^(2) +2x (ac+ bd) + (c^(2) +d^(2))=0 are :

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then