if 0 and 1 are the zeroes of the polynomial F(X)=2x^3-3x^2+ax+b. find the value of a and b
Answers
It is given that both 0 and 1 are the zeroes of the polynomial f(x) = 2x^3 - 3x^2 + ax + b, so numeric value of the polynomial should be 0 on substituting the numeric value of zeroes.
Therefore, f(0) = 0
= > 2(0)^3 - 3(0)^2 + a(0) + b = 0
= > 2(0) - 3(0) + a(0) + b = 0
= > b = 0
Hence the required value of b is 0
When x = 1, f(1) = 0
= > 2(1)^3 - 3(1)^2 + a(1) + b = 0
= > 2(1) - 3(1) + a( 1 ) + 0 = 0 {b=0}
= > 2 - 3 + a = 0
= > - 1 + a = 0
= > a = 1
Hence, a = 1 & b = 0
Polynomial :
f(x) = 2x³-3x²+ax+b
Given zeroes of the f(x) = 0 and 1 .
Put x = 0 in f(x) :
= 2x³-3x²+ax+b
= 2(0)³-30²+a0+b
= 2×0-3×0+0+b
= 0+b
Consider this = 0
b = 0
Then ,
put x = 1 in f(x)
= 2x³-3x²+ax+b
= 2(1)³-3(1)²+a×1+b
= 2-3+a+b
= -1+a+b
Consider this = 0
-1+a+b = 0
Put b = 0 (Obtained above)
-1+a+0= 0
a = 1
The required values of a and b are 1 and 0 respectively.