if 0and1 are the zeroes of the polynomialf(x) =2xcube-3x square+ax+b ,then find the value of a and b
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Step-by-step explanation:
Given :-
0 and 1 are the zeroes of the polynomial
f(x) = 2x³-3x²+ax+b.
To find :-
Find the value of a and b?
Solution :-
Given polynomial is f(x) = 2x³-3x²+ax+b ----(1)
Given zeroes are 0 and 1
We know that
If 0 is a zero of f(x) then it satisfies the given polynomial.i.e. f(0) = 0
Put x = 0 in (1) then
=> f(0) = 2(0)³-3(0)²+a(0)+b = 0
=> 2(0)-3(0)+0+b = 0
=> 0-0+0+b = 0
=> b = 0
If 1 is a zero of f(x) then it satisfies the given polynomial.i.e. f(1) = 0
Put x = 1 in (1) then
=> f(1) = 2(1)³-3(1)²+a(1)+b = 0
=> 2(1)-3(1)+a+b = 0
=> 2-3+a+b = 0
=> -1+a+b = 0
=> -1+a+0 = 0
=> -1+a = 0
=> a = 0+1
=> a = 1
Therefore, a = 1 and b = 0
Answer:-
The values of a and b for the given problem are
1 and 0 respectively.
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