Math, asked by syedanashratamreen, 29 days ago

if 0and1 are the zeroes of the polynomialf(x) =2xcube-3x square+ax+b ,then find the value of a and b​

Answers

Answered by tennetiraj86
3

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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