u/Izzy_26_

I tried Combining the two equations given in the question, this resulted in

(a-6)x² + (2+a)x-6=0

x²-ax+4=0 (given)

These two equations have a common root alpha. USing Cramer's rule

(a²-5a+2)(2a-8)=(4a-18)²

a³-17a²+94a-170=0

How do I solve further? I am not able to calculate the roots of the cubic equation. Also acc to calculator there is only one real value of a that is 5. But the answer key says that there are three answers.

Also is there any other easier method to solve it??

i have got the above two structures, can someone please explain how the third structure is made? Why is there a charge on C, and what about the double bond?

I have been taught to look for these conditions to draw resonating structures.

1. ​lone pair-sigma- vacant orbital

2. ​lone pair-sigma-pi

3. ​pi- sigma-pi

None of them is present in the third one.

Also how many resonating structures of formic acid HCOOH are possible? And how to find out how many resonating structures of a compound ​are possible?

A car which can have constant acceleration of 4 meter per second square and a constant retardation of 8 meter per second square, is travelling on a highway where the maximum speed limit is 72 kilometer per hour. It starts from rest and comes to rest in minimum time T1 after travelling 300 meters and if there is no speed limit, then the minimum time taken is T2 to cover the same distance. Find the value of 4T1/T2.

Here's what I did, is this correct??

The answer key says 5, but I solved assuming that the acceleration can always be either 4 or -8 and never 0.

How do I get started with this one??

We can make cases but that will be lengthy and we have been asked to solve using identities.

I have been taught

mod (x+y) =< mod x + mod y

Equal when xy>=0

mod (x-y) =< mod x + mod y

Equal when xy=<0

How do I solve it using this?? The equation doesn't match with any of the cases

edit- it is supposed to be -4x, instead of 4x sorry for the typo