Polynomial Equation and Inequality

Algebra Level 5

Let p ( x ) , g ( x ) , h ( x ) p(x), g(x), h(x) be a polynomial function such that λ \lambda is one of the real roots of p ( x ) = 0 p(x)=0 . If p ( x ) = ( g ( x ) + h ( x ) ) 2 + c p(x) = (g(x) + h(x))^2 + c where c ≥ 0 c \geq 0 . Find the sum of maximum value and minimum value of c c .

Set

0 13 10 No Solution

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Paul Ryan Longhas
Aug 16, 2015

If c > 0 c > 0 then p ( x ) > 0 p(x) > 0 . So, λ \lambda does not exist.

So, we force to conclude that c = 0 c = 0 to make λ \lambda exist.

Therefore, the sum of the maximum value and minimum value of c c is 0 0 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

There should not be any solution.???

Tarun B - 3 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...