Question

if 2by root of 3 is a zero of a polynomial root of 3x+b then b =​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Since, it is given that

3

and −

3

are the zeroes of the polynomial f(x)=x

3

−4x

2

−3x+12, therefore, (x−

3

) and (x+

3

) are also the zeroes of the given polynomial. Now, consider the product of zeroes as follows:

(x−

3

)(x+

3

)

=(x)

2

−(

3

)

2

(∵a

2

−b

2

=(a+b)(a−b))

=x

2

−3

We now divide x

3

−4x

2

−3x+12 by (x

2

−3) as shown in the above image:

From the division, we observe that the quotient is x−4 and the remainder is 0.

Since x−4 is the quotient,

Hence, the third zero of f(x)=x

3

−4x

2

−3x+12 is 4.

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