00:01
We have given the general value of fx as a x square plus bx plus c and now we have given f of 1 equals to minus 3, f of 2 that is here in minus 11 and then f of minus 2 will give minus 3.
00:24
So the points will be 1 and minus 3, 2 and minus 11, and minus 2 and 3.
00:33
So putting this value in this equation we get x equals to 1 will give a plus b plus c equals to minus 3.
00:43
X equals to 2 will give 4a plus 2 b plus c equals to this is minus 11.
00:49
And now x equals to minus 2 will give 4a minus 2 b plus 2 b plus c equals to, this is minus 11.
00:55
Plus c equals to 3 now augmented matrix will be 1 1 1 minus 3 421 and 4 minus 2 1 will give here here we'll give minus 11 and 3 so these are the points and now we want as much 0 in this matrix as we can so for this subtract r2 minus r3.
01:31
So r2 replaced with r2 minus r3.
01:39
So for this doing this operation we get 1 -1 -1 and we left with here this will be the 0 and minus 4 and here this will be the 0 and 4 minus 2 1.
01:56
And now we can find here this will be also the augmented matrix that is minus 3 minus 11 and 3 now we can see the value of b that is minus 4 b equals to 11 minus 11 that means b equals to 11 divide with 4 now put the value of b in both the equation we'll get here a plus b plus c equals to minus 3 so that means a plus c equals to minus 3 minus 11 divide with 4 also so we get here 4a plus this is minus 2b plus c equals to 3.
02:45
So that means here i'm writing here 4a i can add both of these.
02:54
So adding both of these we get 0 and then this will be the 5a and here this will be the minus b and 2c...