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# Solve this!

Look Closely...it's a quadratic equation. Now find the number of solutions it has.

Note by Diksha Verma
4 years, 5 months ago

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take L.H.S=f(x), and it is easy to show that f'(x)=0; for all x. ie, f(x)= k = f(-a)= 1, so for all x f(x)=1;

- 4 years, 5 months ago

That is a good observation. A simpler approach would be to make common denominator and consider the quadratic polynomial in $$x$$, and easily see that the quadratic coefficient and linear coefficient are both 0.

Staff - 4 years, 5 months ago

If the L.H.S=f(x) (if none of the a,b,c's are equal to each other) then f(x)=1 for all x in R. So f(x)-1=0 for all x in R. Thus f(x)-1=p(x) is the zero polynomial and not a quadratic.

- 4 years, 5 months ago

yes, my answer of -a, -b, -c is not correct as indeed it is an identity function the equation is satisfied for all x belonging to R.

- 4 years, 5 months ago

its, not a quadratic equation as such because it has 3 real roots

- 4 years, 5 months ago

yah! u r right its an identity............ just for confusion.

- 4 years, 5 months ago

I wonder. Did you get this from Praveen Tyagi's FB profile?

- 4 years, 5 months ago

??

- 4 years, 5 months ago

Look, you just liked my comment. lol

- 4 years, 5 months ago

yes

- 4 years, 5 months ago

can u write the solution plsss....

- 4 years, 5 months ago

the roots are -a,-b,-c, assuming a, b, c are distinct real numbers

- 4 years, 5 months ago

how did you got the answer? plzzz explain....i'm not able to solve! :|

- 4 years, 5 months ago

You got 1 on both sides?

- 4 years, 5 months ago

i am not getting a clear solution

- 4 years, 5 months ago

Because if you take lcm of the denominators and expand, and do some algebra there is no x left, infact u get 1=1

- 4 years, 5 months ago

arey.....i took the denominator on the r.h.s. and got 0=0

but m wondering how to get solutions......

this equation is forming an identity i guess

- 4 years, 5 months ago

1=1 implies 1-1=0 so 0=0 :P right?

- 4 years, 5 months ago

very funny.......ha! :/

- 4 years, 5 months ago