An algebra problem by atishay jain

Algebra Level 4

If $f(x)=Ax^4 + Bx^3 + Cx^2 + Dx + E - C$ , such that $A,B,C,D,E$ are in increasing arithmetic progression, where $A$ is positive.

For $f(x) = 0$ , there is at least one imaginary solution.

Then find the number of real roots of $f(x) = 0$ with sign.

no real root none of these 2 positive real roots 1 positive and 1 negative real root 2 real root, both roots negative

1 solution

Atishay Jain
Oct 9, 2017

Since, imaginary roots exist in pairs therefore, there will either be 2 real roots or no real root.

Now, we can see that f(-1) = 0 therefore, f(x) = 0 has 2 real roots.

A, B, C, D and E-C are positive therefore the roots required will be negative as non negative term will remain them as positive. Therefore the function has two negative real roots for f(x) = 0.

An algebra problem by atishay jain

1 solution

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