Algebra

Algebra Level 5

Moderator's edit :

a 2 ( k 2 + 1 ) x 2 − a ( k + 2 ) x 2 + x 4 − 10 x 3 − ( k 2 − k − 1 ) x 2 + 175 x + 650 = 0 a^2(k^2 + 1)x^2 - a(k+2)x^2 + x^4 - 10x^3 - (k^2 -k - 1)x^2 + 175x + 650 = 0

If the sum of two of all the integral roots of the equation above is − 5 -5 , find the values of a ∀ k ∈ R a \forall k \in \mathbb R .


The answer is 1.

Shashwat Avasthi by Shashwat Avasthi , 43, India

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

Kartik Sethi
Jun 1, 2016

We see the coefficient of x² in the given equation a²(k²+1)-a(k+1)-(k²-k+1)= a²k²+a² -ak -2a-k²+k+1= k²(a²-1) + k(1-a) + (a-1)² Since it is true for all k ,therefore this must form a sort of an identity. For that coefficient of k² and k must be zero

Seeing the common root, we get a=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...