24-18B are the zeroes of the polunansial
FG) = x3 - 3x²+x+1 are
(a+b), a and
(a+b), find value of a and b
Answers
Answer:
wow nice very nice
...
good going
good bye
The zero of a polynomial is a value of the variable at which the polynomial equals 0 .
For the said polynomial, we have these equations:
a3−3a2+a+1=0
(a−b)3−3(a−b)2+a−b+1=0
or,a3−3a2b+3ab2−b3−3a2+6ab−3b2+a−b+1=0
3.(a+b)3−3(a+b)2+a+b+1=0
or,a3+3a2b+3ab2+b3−3a2−6ab−3b2+a+b+1=0
Using equations 1 & 2, we get,
−3a2b+3ab2−b3−3b2+6ab−b=0
or, 3a2b−3ab2+b3+3b2−6ab+b=0
Using equations 1 & 3, we get,
3a2b+3ab2+b3−3b2−6ab+b=0
Subtracting last two equations, we get,
6ab2−6b2=0
or, 6b2(a−1)=0
or, b=0, or a=1
Now, putting a=1 in either equation 1 or equation 2, we get,
3b+3b2+b3−3b2−6b+b=0
or, b3−2b=0
or, b(b2−2)=0
or, b=0 , or b=2–√, or b=−2–√
So, we have got a=1 and b=0,2–√,−2–√
Therefore, the zeroes of the said polynomial are 1,1+2–√ and 1−2–√.