Grade 12th passAlgebra

if the roots of the equation 1/x+a + 1/x+b =1/c are equql in magitude but opposite in signs , then their product is (a)- ½ (a squqre+b square) (b)- -1/2 ( a square+ b square) (c)- 1/2ab (d)- -1/2ab

akash kumar mahato

10 Years agoGrade 12th pass

2 Answers

noogler

10 Years ago

aren’t the first and second optins are same?

whatever it may be the correct ans is -1/2(a²+b²)

on solving the given equation into the form ax²+bx+c=0

we get x²+x(a+b+2c)+ab-(a+b)c=0

given the two roots of it are equal in magnitude but opp in sign

i.e, sum of roots =0

from given eq. sum of roots=-b/a=-(a+b+2c)

-(a+b+2c)=0............................a+b/2=c

substitute c=a+b/2 in product of roots = c/a =ab-(a+b)c

on solving it u will get the ans :-)

Rishi Sharma

5 Years ago

Dear Student,
Please find below the solution to your problem.

solving the given equation into the form ax2+bx+c=0
we get x2+x(a+b+2c)+ab-(a+b)c=0
given the two roots of it are equal in magnitude but opp in sign
i.e, sum of roots =0
from given eq. sum of roots=-b/a=-(a+b+2c)
-(a+b+2c)=0............................a+b/2=c
substitute c=a+b/2 in product of roots = c/a =ab-(a+b)c
on solving it u will get the answer

Thanks and Regards