Primitive Modular Quadratics. Part III

Algebra Level 3

Let : { f ( x ) = x 2 − 6 x − 16 g ( x ) = f ( ∣ x ∣ ) h ( x ) = ∣ g ( x ) ∣ \text{Let} : \quad \begin{cases} \quad f(x)=x^2-6x-16 \\ \ \ \ \ g(x)=f(|x|) \\ \ \ \ \ h(x)=|g(x)| \end{cases}

Find the value of ⌊ B ⌋ \lfloor B \rfloor such that the equation h ( x ) − B = 0 h(x)-B=0 has exactly 8 8 real and distinct roots.

0 None of the given choices. No such values of B B exist. 1 2

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Ronak Agarwal
May 21, 2015

At most 6 real and distinct solutions may be present.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Why is it so?

Pi Han Goh - 6 years ago

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Quite clear, once graph of h ( x ) h(x) is sketched !

Sandeep Bhardwaj - 6 years ago

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Done in the same i.e. by graph. I think graphs are important for JEE.

Akshat Sharma - 5 years, 11 months ago

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@Akshat Sharma – yup maximum are 6

Nivedit Jain - 4 years, 2 months ago

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