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

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

Prove that the equation 3x^(5)+15x-18=0 has exactly one real root.

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If the equation a x^2+2b x-3c=0 has no real roots and ((3c)/4) 0 c=0 (d) None of these

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

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for