If `c` is positive and `2a x^2+3b x+5c=0` does not have aby real roots, then prove that `2a-3b+5b>0.`

If the equation x^2-b x+1=0 does not possess real roots, then -3 2 (d) b<-2

If the equation ax^(2)+bx+c=0 does not have 2 distinct real roots and a+c>b, then prove that f(x)>=0,AA x in R

If the equation ax^(2)+bx+c=0 has two positive and real roots,then prove that the eqsition ax^(2)+(b+6a)x+(c+3b)=0 has at least one positive real root.

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

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

IF x^2 + a x + bc = 0 and x^2 + b x + c a = 0 have a common root , then a + b+ c=

If 2x^(3)+ax^(2)+bx+4=0 (a and b are positive real numbers) has 3 real roots,then prove that a+b>=6(2^((1)/(3))+4^((1)/(3)))

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

f(x) is a cubic polynomial x^(3)+ax^(2)+bx+c such that f(x)=0 has three distinct integral roots and f(g(x))=0 does not have real roots,where g(x)=x^(2)+2x-5, the minimum value of a+b+c is