Quadratic and Roots go Hand in Hand

Algebra Level 5

Let $f\left( x \right) =3{ x }^{ 2 }-7x+c$ where $c$ is variable cofficient with $x > \frac 7 6$ .

Determine the value of $c$ such that $f\left( x \right)$ touches $g\left( x \right) =\frac { \sqrt { 12x+49-12c } +7 }{ 6 }$

Give your answer as $\lfloor c \rfloor$ .

Source

Given to me as challenge by me friend Lakshay kumar

The answer is 5.

1 solution

Deepanshu Gupta
Aug 27, 2014

f(x) is an bijection function (since $x>7/6$ .)

so f(x) and g(x) are inverse of each other and Hence f(x) and g(x) must be intersect at $y=x$ .

$f(x)=x$ .

now $D=o$ . (since unique root)

$c=64/12=5.33$ .

Could you please explain more on what is bijection function and how you proceeded to find out that they are the inverse of each other and how you got D=0. could you also suggest any book for theory on polynomials in general. Thanks

Chirag Singapore - 6 years, 3 months ago

Bijection means an function which is one-one and onto , means it's inverse function exist .

D=0 , beacuse f(x)=x has unique solution , hence it must be perfect square !

Nishu sharma - 6 years ago

Quadratic and Roots go Hand in Hand

Source

The answer is 5.

1 solution

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