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Composite Function

IF a,b,c are ...

Question

IF a,b,c are in G.P, then discuss the nature of roots of the equations ax^2 + 2bx +c = 0 and ax^2 + 2bx + 2c = 0.

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a, b, c

are in A.P., then the roots of the equation

a x^{2} + 2 b x + c = 0

Q. If roots of the equation

a x^{2} + 2 (a + b) x + (a + 2 b + c) = 0

are imaginary, then find nature of roots of the equation

a x^{2} + 2 b x + c = 0

a, b, c \in R^{+}

2 b = a + c

, then check the nature of roots of equation

a x^{2} + 2 b x + c = 0

α, β

are the roots of

a x^{2} + 2 b x + c = 0

α + δ

β δ

are the roots of

A x^{2} + 2 B x + C = 0

a \neq b \neq c

& are in H.P then roots of the equation

a x^{2} + 2 b x + c = 0

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