00:00Here I have shown in the reason, this is one equation in our matter and you can understand this much
00:05root means
00:06Alpha plus beta is equal to zero so we have been asked the value of this r so why this
00:13It looks like flour but it is very simple, let's simplify it first, so here we have taken Alshem.
00:18So this becomes two x plus q plus this
00:35x four x squared becomes two x q and plus two x q plus two x p, that is
00:46What can we take by taking two x common plus two x plus q plus p q plus p
00:54Q plus P Q is equal to one upon R
00:57multiply this by h, cross multiply this by h, this becomes,
01:022, 2x plus 2x becomes what it is, 4x, which means 4xr plus p plus q is equal to,
01:14This 4xr plus pr plus qr is equal to, 4x square plus 2xp plus q plus, this, pq,
01:35Now if we move this entire equation to the right side, it will become,
01:414x square plus 2xp plus q plus 2xp plus q minus this, this is what you're going to do,
01:55minus 4xr, taking 2x common from that as well, so it becomes,
01:59minus 2r, what does it become if we multiply, minus 4xr,
02:06We took this common and brought it into this bracket,
02:09This term too, plus pq minus pr minus qr is equal to 0,
02:22Now we have the standard form of the quadratic equation,
02:27ax squared plus bx, let's see,
02:32Here I will under multiply 2, so standard form confusion has come,
02:372p plus 2q minus 4r, we will write this below, so that this confusion does not come,
02:434x square plus x, 2p plus 2q minus 4r plus pq minus pr minus qr is equal to 0,
03:01The standard form of the quadratic equation is given, now we know,
03:06minus of b upon a, this is the sum of the roots of alpha plus beta is equal to minus
03:13of b upon in a,
03:15We're supposed to have the sum of roots of a is 0, which means the minus of b upon a is going to be 0,
03:20So let's write, what does minus b upon a become,
03:23This becomes minus b upon a, across us, minus 2 common,
03:292 of minus, p plus q, and minus 2r upon,
03:41We took this 2 common, so this becomes b plus q minus 2r,
03:45And the b of minus is upon, so this is applying minus, what is the a in upon,
03:494 is equal to sum of root, which is 0,
03:534 This will become order 0, so will it simply become,
03:58This minus 2b goes to this side and becomes 0,
04:02So this goes across to us, p plus q minus 2r is equal to 0,
04:07That is, p plus q is equal to 2r,
04:12So what is the value of r in our end, after solving this,
04:15r is equal to p plus q divided by 2, final answer came,
