Not So Hard!!!

Algebra Level 2

Let a , b , c , d a, b, c, d be the roots of the equation

6 x 4 25 x 3 + 12 x 2 + 25 x + 6 = 0 6{ x }^{ 4 }-25{ x }^{ 3 }+12{ x }^{ 2 }+25x+6=0

Find the value of 6 ( a + b + c + d ) . 6(a+b+c+d).


The answer is 25.

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.

2 solutions

Shriram Lokhande
Jun 19, 2014

according to the viete's formula's if α , β , γ , ϵ \alpha , \beta , \gamma , \epsilon are rots of quartic equation a x 4 + b x 3 + c x 2 + d x + e ax^4+bx^3+cx^2+dx+e then α + β + γ + ϵ = b a \alpha+\beta+\gamma+\epsilon = \frac{-b}{a} hence 6 ( α + β + γ + ϵ ) = 25 6(\alpha+\beta+\gamma+\epsilon) = 25

Very nice!

Heder Oliveira Dias - 6 years, 11 months ago

Did the same ! :D

Reeshabh Ranjan - 6 years, 11 months ago

* quadratic,roots

Dhruv Tyagi - 5 years, 1 month ago
Shubham Sinha
Jul 4, 2014

S u m o f r o o t s : a + b + c + d = 25 6 = 25 6 6 ( a + b + c + d ) = 25 Sum\quad of\quad roots\quad :\quad a+b+c+d\quad =\quad -\quad \frac { -25 }{ 6 } \quad =\quad \frac { 25 }{ 6 } \\ 6\quad (a+b+c+d)\quad =\quad 25

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...