Question

Consider a quadratic equation ax2+2bx+c=0 where a,b,c are positive real numbers. If the equation has no real root, then which of the following is true?

• A. a,b,c cannot be in A.P. or H.P. but can be in G.P.
• B. a,b,c cannot be in G.P. or H.P. but can be in A.P.
• C. a,b,c cannot be in A.P. or G.P. but can be in H.P.
• D. a,b,c cannot be in A.P.,G.P or H.P.

Answer 1

Answer: (C)

a,b,c cannot be in A.P. or G.P. but can be in H.P.

Answer 2

The correct answer is option (C): a,b,c cannot be in A.P. or G.P. but can be in H.P.

In $ax^2+bx+c$, d should be less than 0.

So, $4b^2-4ac=0$

\Rightarrow$$b^2-ac=0

Putting the values of $b=a+\frac{c}{2}$ for A.P,(ac)$^{\frac{1}{2}}$ for G.P and $\frac{2ac}{a+c}$ for H.P, we get the above condition only satisfies H.P.